Nonlinear Dynamics Perspective Of Wolframs New Kind Of Science A Volume V

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Nonlinear Dynamics Perspective Of Wolfram's New Kind Of Science, A (Volume V)

Author : Leon O Chua
Publisher : World Scientific
ISBN 13 : 9814397563
Total Pages : 349 pages
Book Rating : 4.8/5 (143 download)

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Book Synopsis Nonlinear Dynamics Perspective Of Wolfram's New Kind Of Science, A (Volume V) by : Leon O Chua

Download or read book Nonlinear Dynamics Perspective Of Wolfram's New Kind Of Science, A (Volume V) written by Leon O Chua and published by World Scientific. This book was released on 2012-03-13 with total page 349 pages. Available in PDF, EPUB and Kindle. Book excerpt: This penultimate volume contains numerous original, elegant, and surprising results in 1-dimensional cellular automata. Perhaps the most exciting, if not shocking, new result is the discovery that only 82 local rules, out of 256, suffice to predict the time evolution of any of the remaining 174 local rules from an arbitrary initial bit-string configuration. This is contrary to the well-known folklore that 256 local rules are necessary, leading to the new concept of quasi-global equivalence.Another surprising result is the introduction of a simple, yet explicit, infinite bit string called the super string S, which contains all random bit strings of finite length as sub-strings. As an illustration of the mathematical subtlety of this amazing discrete testing signal, the super string S is used to prove mathematically, in a trivial and transparent way, that rule 170 is as chaotic as a coin toss.Yet another unexpected new result, among many others, is the derivation of an explicit basin tree generation formula which provides an analytical relationship between the basin trees of globally-equivalent local rules. This formula allows the symbolic, rather than numerical, generation of the time evolution of any local rule corresponding to any initial bit-string configuration, from one of the 88 globally-equivalent local rules.But perhaps the most provocative idea is the proposal for adopting rule 137, over its three globally-equivalent siblings, including the heretofore more well-known rule 110, as the prototypical universal Turing machine.

Nonlinear Dynamics Perspective Of Wolfram's New Kind Of Science, A (Volume Iv)

Author : Leon O Chua
Publisher : World Scientific
ISBN 13 : 9814464430
Total Pages : 404 pages
Book Rating : 4.8/5 (144 download)

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Book Synopsis Nonlinear Dynamics Perspective Of Wolfram's New Kind Of Science, A (Volume Iv) by : Leon O Chua

Download or read book Nonlinear Dynamics Perspective Of Wolfram's New Kind Of Science, A (Volume Iv) written by Leon O Chua and published by World Scientific. This book was released on 2011-04-06 with total page 404 pages. Available in PDF, EPUB and Kindle. Book excerpt: Volume IV continues the author's odyssey on l-D cellular automata as chronicled in Volumes I, II and III, by uncovering a novel quasi-ergodicity phenomenon involving orbits meandering among omega-limit orbits of complex (group 5) and hyper (group 6) Bernoulli rules. This discovery is embellished with analytical formulas characterizing the fractal properties of characteristic functions, as well as explicit formulas for generating colorful and pedagogically revealing isomorphic basin tree diagrams. Many new results were derived and proved by uncovering subtle symmetries endowed by various subsets of the 256 Boolean cubes. For the first time, rigorous analyses were used to identify 67, out off 256, local rules whose asymptotic behaviors consist of robust period-l orbits. The highlight of this continuing odyssey is the discovery of an isolated period-3240 Isle of Eden hidden among the dense omega-limit orbits of Wolfram's remarkable “random number generating” rule 30. This is the largest gem known to-date and readers are challenged to uncover even larger ones.

A Nonlinear Dynamics Perspective of Wolfram's New Kind of Science

Author : Leon O. Chua
Publisher : World Scientific
ISBN 13 : 9814390526
Total Pages : 349 pages
Book Rating : 4.8/5 (143 download)

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Book Synopsis A Nonlinear Dynamics Perspective of Wolfram's New Kind of Science by : Leon O. Chua

Download or read book A Nonlinear Dynamics Perspective of Wolfram's New Kind of Science written by Leon O. Chua and published by World Scientific. This book was released on 2012 with total page 349 pages. Available in PDF, EPUB and Kindle. Book excerpt: This penultimate volume contains numerous original, elegant, and surprising results in 1-dimensional cellular automata. Perhaps the most exciting, if not shocking, new result is the discovery that only 82 local rules, out of 256, suffice to predict the time evolution of any of the remaining 174 local rules from an arbitrary initial bit-string configuration. This is contrary to the well-known folklore that 256 local rules are necessary, leading to the new concept of quasi-global equivalence . Another surprising result is the introduction of a simple, yet explicit, infinite bit string called the super string S, which contains all random bit strings of finite length as sub-strings. As an illustration of the mathematical subtlety of this amazing discrete testing signal, the super string S is used to prove mathematically, in a trivial and transparent way, that rule 170 is as chaotic as a coin toss . Yet another unexpected new result, among many others, is the derivation of an explicit basin tree generation formula which provides an analytical relationship between the basin trees of globally-equivalent local rules. This formula allows the symbolic, rather than numerical, generation of the time evolution of any local rule corresponding to any initial bit-string configuration, from one of the 88 globally-equivalent local rules. But perhaps the most provocative idea is the proposal for adopting rule 137, over its three globally-equivalent siblings, including the heretofore more well-known rule 110, as the prototypical universal Turing machine .

Nonlinear Dynamics Perspective Of Wolfram's New Kind Of Science, A - Volume Iii

Author : Leon O Chua
Publisher : World Scientific
ISBN 13 : 9814468940
Total Pages : 357 pages
Book Rating : 4.8/5 (144 download)

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Book Synopsis Nonlinear Dynamics Perspective Of Wolfram's New Kind Of Science, A - Volume Iii by : Leon O Chua

Download or read book Nonlinear Dynamics Perspective Of Wolfram's New Kind Of Science, A - Volume Iii written by Leon O Chua and published by World Scientific. This book was released on 2009-08-11 with total page 357 pages. Available in PDF, EPUB and Kindle. Book excerpt: Volume III continues the author's quest for developing a pedagogical, self-contained, yet rigorous analytical theory of 1-D cellular automata via a nonlinear dynamics perspective. Using carefully conceived and illuminating color graphics, the global dynamical behaviors of the 50 (out of 256) local rules that have not yet been covered in Volumes I and II are exposed via their stunningly revealing basin tree diagrams. The Bernoulli στ-shift dynamics discovered in Volume II is generalized to hold for all 50 (or 18 globally equivalent) local rules via complex and hyper Bernoulli wave dynamics. Explicit global state transition formulas derived for rules 60, 90, 105, and 150 reveal a new scale-free phenomenon. The most surprising new result unveiled in this volume is the “Isle of Eden” found hidden in most (almost 90%) of the 256 local rules. Readers are challenged to hunt for long-period, isolated Isles of Eden. These are rare gems waiting to be discovered.

Nonlinear Dynamics Perspective Of Wolfram's New Kind Of Science, A (In 2 Volumes) - Volume I

Author : Leon O Chua
Publisher : World Scientific
ISBN 13 : 9814478687
Total Pages : 397 pages
Book Rating : 4.8/5 (144 download)

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Book Synopsis Nonlinear Dynamics Perspective Of Wolfram's New Kind Of Science, A (In 2 Volumes) - Volume I by : Leon O Chua

Download or read book Nonlinear Dynamics Perspective Of Wolfram's New Kind Of Science, A (In 2 Volumes) - Volume I written by Leon O Chua and published by World Scientific. This book was released on 2006-06-08 with total page 397 pages. Available in PDF, EPUB and Kindle. Book excerpt: This novel book introduces cellular automata from a rigorous nonlinear dynamics perspective. It supplies the missing link between nonlinear differential and difference equations to discrete symbolic analysis. A surprisingly useful interpretations of cellular automata in terms of neural networks is also given. The book provides a scientifically sound and original analysis, and classifications of the empirical results presented in Wolfram's monumental ';New Kind of Science.';

Nonlinear Dynamics Perspective Of Wolfram's New Kind Of Science, A (Volume Vi)

Author : Leon O Chua
Publisher : World Scientific
ISBN 13 : 9814460893
Total Pages : 579 pages
Book Rating : 4.8/5 (144 download)

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Book Synopsis Nonlinear Dynamics Perspective Of Wolfram's New Kind Of Science, A (Volume Vi) by : Leon O Chua

Download or read book Nonlinear Dynamics Perspective Of Wolfram's New Kind Of Science, A (Volume Vi) written by Leon O Chua and published by World Scientific. This book was released on 2013-07-10 with total page 579 pages. Available in PDF, EPUB and Kindle. Book excerpt: This invaluable volume ends the quest to uncover the secret recipes for predicting the long-term evolution of a ring of identical elementary cells where the binary state of each cell during each generation of an attractor (i.e. after the transients had disappeared) is determined uniquely by the state of its left and right neighbors in the previous generation, as decreed by one of 256 truth tables. As befitting the contents aimed at school children, it was found pedagogically appealing to code each truth table by coloring each of the 8 vertices of a cubical graph in red (for binary state 1), or blue (for binary state 0), forming a toy universe of 256 Boolean cubes, each bearing a different vertex color combination.The corresponding collection of 256 distinct Boolean cubes are then segegrated logically into 6 distinct groups where members from each group share certain common dynamics which allow the long-term evolution of the color configuration of each bit string, of arbitrary length, to be predicted painlessly, via a toy-like gaming procedure, without involving any calculation. In particular, the evolution of any bit string bearing any initial color configuration which resides in any one of the possibly many distinct attractors, can be systematically predicted, by school children who are yet to learn arithmetic, via a simple recipe, for any Boolean cube belonging to group 1, 2, 3, or 4. The simple recipe for predicting the time-asymptotic behaviors of Boolean cubes belonging to groups 1, 2, and 3 has been covered in Vols. I, II, ..., V.This final volume continues the recipe for each of the 108, out of 256, local rules, dubbed the Bernoulli rules, belonging to group 4. Here, for almost half of the toy universe, surprisingly simple recipes involving only the following three pieces of information are derived in Vol. VI; namely, a positive integer τ, a positive, or negative, integer σ, and a sign parameter β > 0, or β 0. In particular, given any color configuration belonging to an attractor of any one of the 108 Boolean cubes from group 4, any child can predict the color configuration after τ generations, without any computation, by merely shifting each cell σ bits to the left (resp. right) if σ 0 (resp. σ

Nonlinear Dynamics Perspective Of Wolfram's New Kind Of Science, A (In 2 Volumes) - Volume Ii

Author : Leon O Chua
Publisher : World Scientific
ISBN 13 : 9814478695
Total Pages : 598 pages
Book Rating : 4.8/5 (144 download)

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Book Synopsis Nonlinear Dynamics Perspective Of Wolfram's New Kind Of Science, A (In 2 Volumes) - Volume Ii by : Leon O Chua

Download or read book Nonlinear Dynamics Perspective Of Wolfram's New Kind Of Science, A (In 2 Volumes) - Volume Ii written by Leon O Chua and published by World Scientific. This book was released on 2007-07-10 with total page 598 pages. Available in PDF, EPUB and Kindle. Book excerpt: This novel book introduces cellular automata from a rigorous nonlinear dynamics perspective. It supplies the missing link between nonlinear differential and difference equations to discrete symbolic analysis. A surprisingly useful interpretations of cellular automata in terms of neural networks is also given. The book provides a scientifically sound and original analysis, and classifications of the empirical results presented in Wolfram's monumental ';New Kind of Science.';

A New Kind of Science

Author : Stephen Wolfram
Publisher :
ISBN 13 : 9780713991161
Total Pages : 1197 pages
Book Rating : 4.9/5 (911 download)

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Book Synopsis A New Kind of Science by : Stephen Wolfram

Download or read book A New Kind of Science written by Stephen Wolfram and published by . This book was released on 2002 with total page 1197 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work presents a series of dramatic discoveries never before made public. Starting from a collection of simple computer experiments---illustrated in the book by striking computer graphics---Wolfram shows how their unexpected results force a whole new way of looking at the operation of our universe. Wolfram uses his approach to tackle a remarkable array of fundamental problems in science: from the origin of the Second Law of thermodynamics, to the development of complexity in biology, the computational limitations of mathematics, the possibility of a truly fundamental theory of physics, and the interplay between free will and determinism.

Control Of Imperfect Nonlinear Electromechanical Large Scale Systems: From Dynamics To Hardware Implementation

Author : Luigi Fortuna
Publisher : World Scientific
ISBN 13 : 9813227257
Total Pages : 147 pages
Book Rating : 4.8/5 (132 download)

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Book Synopsis Control Of Imperfect Nonlinear Electromechanical Large Scale Systems: From Dynamics To Hardware Implementation by : Luigi Fortuna

Download or read book Control Of Imperfect Nonlinear Electromechanical Large Scale Systems: From Dynamics To Hardware Implementation written by Luigi Fortuna and published by World Scientific. This book was released on 2017-05-19 with total page 147 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book focuses on a class of uncertain systems that are called imperfect, and shows how much systems can regularly work if an appropriate control strategy is adopted. Along with some practical well studied examples, a formalization of the models for imperfect system is considered and a control strategy is proposed. Experimental case studies on electromechanical systems are also included.New concepts, experimental innovative circuits and laboratory details allow the reader to implement at low cost the outlined strategy. Emergent topics in nonlinear device realization are emphasized with the aim to allow researchers and students to perform experiments with large scale electromechanical systems. Moreover, the possibility of using imperfections and noise to generate nonlinear strange behavior is discussed.

Topology and Dynamics of Chaos

Author : Christophe Letellier
Publisher : World Scientific
ISBN 13 : 9814434868
Total Pages : 362 pages
Book Rating : 4.8/5 (144 download)

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Book Synopsis Topology and Dynamics of Chaos by : Christophe Letellier

Download or read book Topology and Dynamics of Chaos written by Christophe Letellier and published by World Scientific. This book was released on 2013 with total page 362 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book surveys how chaotic behaviors can be described with topological tools and how this approach occurred in chaos theory. Some modern applications are included. The contents are mainly devoted to topology, the main field of Robert Gilmore's works in dynamical systems. They include a review on the topological analysis of chaotic dynamics, works done in the past as well as the very latest issues. Most of the contributors who published during the 90's, including the very well-known scientists Otto RAssler, Ren(r) Lozi and Joan Birman, have made a significant impact on chaos theory, discrete chaos, and knot theory, respectively. Very few books cover the topological approach for investigating nonlinear dynamical systems. The present book will provide not only some historical OCo not necessarily widely known OCo contributions (about the different types of chaos introduced by RAssler and not just the RAssler attractor; Gumowski and Mira's contributions in electronics; Poincar(r)'s heritage in nonlinear dynamics) but also some recent applications in laser dynamics, biology,

Deterministic Chaos In One Dimensional Continuous Systems

Author : Jan Awrejcewicz
Publisher : World Scientific
ISBN 13 : 9814719714
Total Pages : 577 pages
Book Rating : 4.8/5 (147 download)

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Book Synopsis Deterministic Chaos In One Dimensional Continuous Systems by : Jan Awrejcewicz

Download or read book Deterministic Chaos In One Dimensional Continuous Systems written by Jan Awrejcewicz and published by World Scientific. This book was released on 2016-03-14 with total page 577 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book focuses on the computational analysis of nonlinear vibrations of structural members (beams, plates, panels, shells), where the studied dynamical problems can be reduced to the consideration of one spatial variable and time. The reduction is carried out based on a formal mathematical approach aimed at reducing the problems with infinite dimension to finite ones. The process also includes a transition from governing nonlinear partial differential equations to a set of finite number of ordinary differential equations.Beginning with an overview of the recent results devoted to the analysis and control of nonlinear dynamics of structural members, placing emphasis on stability, buckling, bifurcation and deterministic chaos, simple chaotic systems are briefly discussed. Next, bifurcation and chaotic dynamics of the Euler-Bernoulli and Timoshenko beams including the geometric and physical nonlinearity as well as the elastic-plastic deformations are illustrated. Despite the employed classical numerical analysis of nonlinear phenomena, the various wavelet transforms and the four Lyapunov exponents are used to detect, monitor and possibly control chaos, hyper-chaos, hyper-hyper-chaos and deep chaos exhibited by rectangular plate-strips and cylindrical panels.The book is intended for post-graduate and doctoral students, applied mathematicians, physicists, teachers and lecturers of universities and companies dealing with a nonlinear dynamical system, as well as theoretically inclined engineers of mechanical and civil engineering.

Modeling Love Dynamics

Author : Sergio E. T. Al RINALDI
Publisher : World Scientific
ISBN 13 : 9814696323
Total Pages : 256 pages
Book Rating : 4.8/5 (146 download)

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Book Synopsis Modeling Love Dynamics by : Sergio E. T. Al RINALDI

Download or read book Modeling Love Dynamics written by Sergio E. T. Al RINALDI and published by World Scientific. This book was released on 2015-10-22 with total page 256 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book shows, for the very first time, how love stories -- a vital issue in our lives -- can be tentatively described with classical mathematics. Focus is on the derivation and analysis of reliable models that allow one to formally describe the expected evolution of love affairs from the initial state of indifference to the final romantic regime. The models are in full agreement with the basic philosophical principles of love psychology. Eight chapters are theoretically oriented and discuss the romantic relationships between important classes of individuals identified by particular psychological traits. The remaining chapters are devoted to case studies described in classical poems or in worldwide famous films.

Wave Momentum And Quasi-particles In Physical Acoustics

Author : Gerard A Maugin
Publisher : World Scientific
ISBN 13 : 9814663808
Total Pages : 250 pages
Book Rating : 4.8/5 (146 download)

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Book Synopsis Wave Momentum And Quasi-particles In Physical Acoustics by : Gerard A Maugin

Download or read book Wave Momentum And Quasi-particles In Physical Acoustics written by Gerard A Maugin and published by World Scientific. This book was released on 2015-03-26 with total page 250 pages. Available in PDF, EPUB and Kindle. Book excerpt: This unique volume presents an original approach to physical acoustics with additional emphasis on the most useful surface acoustic waves on solids. The study is based on foundational work of Léon Brillouin, and application of the celebrated invariance theorem of Emmy Noether to an element of volume that is representative of the wave motion.This approach provides an easy interpretation of typical wave motions of physical acoustics in bulk, at surfaces, and across interfaces, in the form of the motion of associated quasi-particles. This type of motion, Newtonian or not, depends on the wave motion considered, and on the original modeling of the continuum that supports it. After a thoughtful review of Brillouin's fundamental ideas related to radiative stresses, wave momentum and action, and the necessary reminder on modern nonlinear continuum thermomechanics, invariance theory and techniques of asymptotics, a variety of situations and models illustrates the power and richness of the approach and its strong potential in applications. Elasticity, piezoelectricity and new models of continua with nonlinearity, viscosity and some generalized features (microstructure, weak or strong nonlocality) or unusual situations (bounding surface with energy, elastic thin film glued on a surface waveguide), are considered, exhibiting thus the versatility of the approach.This original book offers an innovative vision and treatment of the problems of wave propagation in deformable solids. It opens up new horizons in the theoretical and applied facets of physical acoustics.

Development of Memristor Based Circuits

Author : Andrew L. Fitch
Publisher : World Scientific
ISBN 13 : 9814383392
Total Pages : 133 pages
Book Rating : 4.8/5 (143 download)

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Book Synopsis Development of Memristor Based Circuits by : Andrew L. Fitch

Download or read book Development of Memristor Based Circuits written by Andrew L. Fitch and published by World Scientific. This book was released on 2013 with total page 133 pages. Available in PDF, EPUB and Kindle. Book excerpt: In 1971, Leon O. Chua presented the formulation of a memristor, which was postulated as the fourth circuit element in electrical circuit theory OCo one that could join the existing core group of elements: capacitor, resistor and inductor. For over thirty years, the memristor had held no significance in circuit theory. Then in 2008, a group of scientists from Hewlett-Packard Labs (HP) developed a working memristor. Although the solid state implementation of the memristor inspired appreciable interest in developing applications, memristors are not yet available on the market to date. HP labs do not expect to introduce memristors in a product for a few more years. Therefore, the development of memristor based circuits is essential for further experimental research on the applications.Combining an overview, tutorial and technical articles, the book describes the state-of-the-art research on significant issues in the field. Examples of memristor mimicking circuits are presented, and applications of memristor based circuits addressed.

Chaos in Nature

Author : Christophe Letellier
Publisher : World Scientific
ISBN 13 : 9814374431
Total Pages : 393 pages
Book Rating : 4.8/5 (143 download)

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Book Synopsis Chaos in Nature by : Christophe Letellier

Download or read book Chaos in Nature written by Christophe Letellier and published by World Scientific. This book was released on 2013 with total page 393 pages. Available in PDF, EPUB and Kindle. Book excerpt: Chaos theory deals with the description of motion (in a general sense) which cannot be predicted in the long term although produced by deterministic system, as well exemplified by meteorological phenomena. It directly comes from the Lunar theory OCo a three-body problem OCo and the difficulty encountered by astronomers to accurately predict the long-term evolution of the Moon using OC NewtonianOCO mechanics. Henri Poincar(r)''s deep intuitions were at the origin of chaos theory. They also led the meteorologist Edward Lorenz to draw the first chaotic attractor ever published. But the main idea consists of plotting a curve representative of the system evolution rather than finding an analytical solution as commonly done in classical mechanics. Such a novel approach allows the description of population interactions and the solar activity as well. Using the original sources, the book draws on the history of the concepts underlying chaos theory from the 17th century to the last decade, and by various examples, show how general is this theory in a wide range of applications: meteorology, chemistry, populations, astrophysics, biomedicine, et

Integral Dynamical Models: Singularities, Signals And Control

Author : Denis Sidorov
Publisher : World Scientific
ISBN 13 : 9814619205
Total Pages : 258 pages
Book Rating : 4.8/5 (146 download)

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Book Synopsis Integral Dynamical Models: Singularities, Signals And Control by : Denis Sidorov

Download or read book Integral Dynamical Models: Singularities, Signals And Control written by Denis Sidorov and published by World Scientific. This book was released on 2014-09-05 with total page 258 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume provides a broad introduction to nonlinear integral dynamical models and new classes of evolutionary integral equations. It may be used as an advanced textbook by postgraduate students to study integral dynamical models and their applications in machine learning, electrical and electronic engineering, operations research and image analysis.

Elements of Mathematical Theory of Evolutionary Equations in Banach Spaces

Author : Anatoly M. Samoilenko
Publisher : World Scientific
ISBN 13 : 9814434833
Total Pages : 408 pages
Book Rating : 4.8/5 (144 download)

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Book Synopsis Elements of Mathematical Theory of Evolutionary Equations in Banach Spaces by : Anatoly M. Samoilenko

Download or read book Elements of Mathematical Theory of Evolutionary Equations in Banach Spaces written by Anatoly M. Samoilenko and published by World Scientific. This book was released on 2013 with total page 408 pages. Available in PDF, EPUB and Kindle. Book excerpt: Evolutionary equations are studied in abstract Banach spaces and in spaces of bounded number sequences. For linear and nonlinear difference equations, which are defined on finite-dimensional and infinite-dimensional tori, the problem of reducibility is solved, in particular, in neighborhoods of their invariant sets, and the basics for a theory of invariant tori and bounded semi-invariant manifolds are established. Also considered are the questions on existence and approximate construction of periodic solutions for difference equations in infinite-dimensional spaces and the problem of extendibility of the solutions in degenerate cases. For nonlinear differential equations in spaces of bounded number sequences, new results are obtained in the theory of countable-point boundary-value problems. The book contains new mathematical results that will be useful towards advances in nonlinear mechanics and theoretical physics.