From Combinatorics To Dynamical Systems

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Ergodic Theory and Dynamical Systems in their Interactions with Arithmetics and Combinatorics

Author : Sébastien Ferenczi
Publisher : Springer
ISBN 13 : 3319749080
Total Pages : 434 pages
Book Rating : 4.3/5 (197 download)

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Book Synopsis Ergodic Theory and Dynamical Systems in their Interactions with Arithmetics and Combinatorics by : Sébastien Ferenczi

Download or read book Ergodic Theory and Dynamical Systems in their Interactions with Arithmetics and Combinatorics written by Sébastien Ferenczi and published by Springer. This book was released on 2018-06-15 with total page 434 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book concentrates on the modern theory of dynamical systems and its interactions with number theory and combinatorics. The greater part begins with a course in analytic number theory and focuses on its links with ergodic theory, presenting an exhaustive account of recent research on Sarnak's conjecture on Möbius disjointness. Selected topics involving more traditional connections between number theory and dynamics are also presented, including equidistribution, homogenous dynamics, and Lagrange and Markov spectra. In addition, some dynamical and number theoretical aspects of aperiodic order, some algebraic systems, and a recent development concerning tame systems are described.

Representation Theory, Dynamical Systems, and Asymptotic Combinatorics

Author : V. Kaimanovich
Publisher : American Mathematical Soc.
ISBN 13 : 0821872893
Total Pages : 258 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Representation Theory, Dynamical Systems, and Asymptotic Combinatorics by : V. Kaimanovich

Download or read book Representation Theory, Dynamical Systems, and Asymptotic Combinatorics written by V. Kaimanovich and published by American Mathematical Soc.. This book was released on 2011-11-09 with total page 258 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume, devoted to the 70th birthday of the well-known St. Petersburg mathematician A. M. Vershik, contains a collection of articles by participants in the conference "Representation Theory, Dynamical Systems, and Asymptotic Combinatorics", held in St. Petersburg in June of 2004. The book is suitable for graduate students and researchers interested in combinatorial and dynamical aspects of group representation theory.

From Combinatorics to Dynamical Systems

Author : Frederic Fauvet
Publisher : Walter de Gruyter
ISBN 13 : 3110200007
Total Pages : 257 pages
Book Rating : 4.1/5 (12 download)

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Book Synopsis From Combinatorics to Dynamical Systems by : Frederic Fauvet

Download or read book From Combinatorics to Dynamical Systems written by Frederic Fauvet and published by Walter de Gruyter. This book was released on 2008-08-22 with total page 257 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains nine refereed research papers in various areas from combinatorics to dynamical systems, with computer algebra as an underlying and unifying theme. Topics covered include irregular connections, rank reduction and summability of solutions of differential systems, asymptotic behaviour of divergent series, integrability of Hamiltonian systems, multiple zeta values, quasi-polynomial formalism, Padé approximants related to analytic integrability, hybrid systems. The interactions between computer algebra, dynamical systems and combinatorics discussed in this volume should be useful for both mathematicians and theoretical physicists who are interested in effective computation.

Substitutions in Dynamics, Arithmetics and Combinatorics

Author : N. Pytheas Fogg
Publisher : Springer
ISBN 13 : 3540457143
Total Pages : 404 pages
Book Rating : 4.5/5 (44 download)

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Book Synopsis Substitutions in Dynamics, Arithmetics and Combinatorics by : N. Pytheas Fogg

Download or read book Substitutions in Dynamics, Arithmetics and Combinatorics written by N. Pytheas Fogg and published by Springer. This book was released on 2003-10-24 with total page 404 pages. Available in PDF, EPUB and Kindle. Book excerpt: A certain category of infinite strings of letters on a finite alphabet is presented here, chosen among the 'simplest' possible one may build, both because they are very deterministic and because they are built by simple rules (a letter is replaced by a word, a sequence is produced by iteration). These substitutive sequences have a surprisingly rich structure. The authors describe the concepts of quantity of natural interactions, with combinatorics on words, ergodic theory, linear algebra, spectral theory, geometry of tilings, theoretical computer science, diophantine approximation, trancendence, graph theory. This volume fulfils the need for a reference on the basic definitions and theorems, as well as for a state-of-the-art survey of the more difficult and unsolved problems.

Differential Equations and Dynamical Systems

Author : D. Bahuguna
Publisher : Alpha Science Int'l Ltd.
ISBN 13 : 9788173195884
Total Pages : 246 pages
Book Rating : 4.1/5 (958 download)

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Book Synopsis Differential Equations and Dynamical Systems by : D. Bahuguna

Download or read book Differential Equations and Dynamical Systems written by D. Bahuguna and published by Alpha Science Int'l Ltd.. This book was released on 2005 with total page 246 pages. Available in PDF, EPUB and Kindle. Book excerpt: Fifteen chapters from eminent researchers working in the area of differential equations and dynamical systems covering all relevant subjects, ranging from wavelets and their applications, to second order evolution equations.

Combinatorial Dynamics And Entropy In Dimension One

Author : Alseda Luis
Publisher : World Scientific Publishing Company
ISBN 13 : 9814553220
Total Pages : 344 pages
Book Rating : 4.8/5 (145 download)

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Book Synopsis Combinatorial Dynamics And Entropy In Dimension One by : Alseda Luis

Download or read book Combinatorial Dynamics And Entropy In Dimension One written by Alseda Luis and published by World Scientific Publishing Company. This book was released on 1993-06-04 with total page 344 pages. Available in PDF, EPUB and Kindle. Book excerpt: In last thirty years an explosion of interest in the study of nonlinear dynamical systems occured. The theory of one-dimensional dynamical systems has grown out in many directions. One of them has its roots in the Sharkovski0 Theorem. This beautiful theorem describes the possible sets of periods of all cycles of maps of an interval into itself. Another direction has its main objective in measuring the complexity of a system, or the amount of chaos present in it. A good way of doing this is to compute topological entropy of the system. The aim of this book is to provide graduate students and researchers with a unified and detailed exposition of these developments for interval and circle maps. Many comments are added referring to related problems, and historical remarks are made. Request Inspection Copy

Substitution Dynamical Systems - Spectral Analysis

Author : Martine Queffélec
Publisher : Springer
ISBN 13 : 3540480889
Total Pages : 252 pages
Book Rating : 4.5/5 (44 download)

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Book Synopsis Substitution Dynamical Systems - Spectral Analysis by : Martine Queffélec

Download or read book Substitution Dynamical Systems - Spectral Analysis written by Martine Queffélec and published by Springer. This book was released on 2006-11-14 with total page 252 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Combinations of Complex Dynamical Systems

Author : Kevin M. Pilgrim
Publisher : Springer
ISBN 13 : 3540399364
Total Pages : 120 pages
Book Rating : 4.5/5 (43 download)

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Book Synopsis Combinations of Complex Dynamical Systems by : Kevin M. Pilgrim

Download or read book Combinations of Complex Dynamical Systems written by Kevin M. Pilgrim and published by Springer. This book was released on 2003-12-12 with total page 120 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work is a research-level monograph whose goal is to develop a general combination, decomposition, and structure theory for branched coverings of the two-sphere to itself, regarded as the combinatorial and topological objects which arise in the classification of certain holomorphic dynamical systems on the Riemann sphere. It is intended for researchers interested in the classification of those complex one-dimensional dynamical systems which are in some loose sense tame. The program is motivated by the dictionary between the theories of iterated rational maps and Kleinian groups.

An Introduction to Sequential Dynamical Systems

Author : Henning Mortveit
Publisher : Springer Science & Business Media
ISBN 13 : 0387498796
Total Pages : 248 pages
Book Rating : 4.3/5 (874 download)

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Book Synopsis An Introduction to Sequential Dynamical Systems by : Henning Mortveit

Download or read book An Introduction to Sequential Dynamical Systems written by Henning Mortveit and published by Springer Science & Business Media. This book was released on 2007-11-27 with total page 248 pages. Available in PDF, EPUB and Kindle. Book excerpt: This introductory text to the class of Sequential Dynamical Systems (SDS) is the first textbook on this timely subject. Driven by numerous examples and thought-provoking problems throughout, the presentation offers good foundational material on finite discrete dynamical systems, which then leads systematically to an introduction of SDS. From a broad range of topics on structure theory - equivalence, fixed points, invertibility and other phase space properties - thereafter SDS relations to graph theory, classical dynamical systems as well as SDS applications in computer science are explored. This is a versatile interdisciplinary textbook.

Complex and Adaptive Dynamical Systems

Author : Claudius Gros
Publisher : Springer
ISBN 13 : 3319162659
Total Pages : 422 pages
Book Rating : 4.3/5 (191 download)

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Book Synopsis Complex and Adaptive Dynamical Systems by : Claudius Gros

Download or read book Complex and Adaptive Dynamical Systems written by Claudius Gros and published by Springer. This book was released on 2015-04-01 with total page 422 pages. Available in PDF, EPUB and Kindle. Book excerpt: This primer offers readers an introduction to the central concepts that form our modern understanding of complex and emergent behavior, together with detailed coverage of accompanying mathematical methods. All calculations are presented step by step and are easy to follow. This new fourth edition has been fully reorganized and includes new chapters, figures and exercises. The core aspects of modern complex system sciences are presented in the first chapters, covering network theory, dynamical systems, bifurcation and catastrophe theory, chaos and adaptive processes, together with the principle of self-organization in reaction-diffusion systems and social animals. Modern information theoretical principles are treated in further chapters, together with the concept of self-organized criticality, gene regulation networks, hypercycles and coevolutionary avalanches, synchronization phenomena, absorbing phase transitions and the cognitive system approach to the brain. Technical course prerequisites are the standard mathematical tools for an advanced undergraduate course in the natural sciences or engineering. Each chapter includes exercises and suggestions for further reading, and the solutions to all exercises are provided in the last chapter. From the reviews of previous editions: This is a very interesting introductory book written for a broad audience of graduate students in natural sciences and engineering. It can be equally well used both for teac hing and self-education. Very well structured and every topic is illustrated with simple and motivating examples. This is a true guidebook to the world of complex nonlinear phenomena. (Ilya Pavlyukevich, Zentralblatt MATH, Vol. 1146, 2008) Claudius Gros’ Complex and Adaptive Dynamical Systems: A Primer is a welcome addition to the literature. A particular strength of the book is its emphasis on analytical techniques for studying complex systems. (David P. Feldman, Physics Today, July, 2009).

Recurrence in Ergodic Theory and Combinatorial Number Theory

Author : Harry Furstenberg
Publisher : Princeton University Press
ISBN 13 : 1400855160
Total Pages : 216 pages
Book Rating : 4.4/5 (8 download)

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Book Synopsis Recurrence in Ergodic Theory and Combinatorial Number Theory by : Harry Furstenberg

Download or read book Recurrence in Ergodic Theory and Combinatorial Number Theory written by Harry Furstenberg and published by Princeton University Press. This book was released on 2014-07-14 with total page 216 pages. Available in PDF, EPUB and Kindle. Book excerpt: Topological dynamics and ergodic theory usually have been treated independently. H. Furstenberg, instead, develops the common ground between them by applying the modern theory of dynamical systems to combinatories and number theory. Originally published in 1981. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.

The Dynamical System Generated by the 3n+1 Function

Author : Günther J. Wirsching
Publisher : Springer
ISBN 13 : 3540696776
Total Pages : 166 pages
Book Rating : 4.5/5 (46 download)

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Book Synopsis The Dynamical System Generated by the 3n+1 Function by : Günther J. Wirsching

Download or read book The Dynamical System Generated by the 3n+1 Function written by Günther J. Wirsching and published by Springer. This book was released on 2006-11-14 with total page 166 pages. Available in PDF, EPUB and Kindle. Book excerpt: The 3n+1 function T is defined by T(n)=n/2 for n even, and T(n)=(3n+1)/2 for n odd. The famous 3n+1 conjecture, which remains open, states that, for any starting number n>0, iterated application of T to n eventually produces 1. After a survey of theorems concerning the 3n+1 problem, the main focus of the book are 3n+1 predecessor sets. These are analyzed using, e.g., elementary number theory, combinatorics, asymptotic analysis, and abstract measure theory. The book is written for any mathematician interested in the 3n+1 problem, and in the wealth of mathematical ideas employed to attack it.

Representation Theory, Dynamical Systems, and Asymptotic Combinatorics

Author : V. Kaimanovich
Publisher :
ISBN 13 : 9781470418243
Total Pages : 258 pages
Book Rating : 4.4/5 (182 download)

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Book Synopsis Representation Theory, Dynamical Systems, and Asymptotic Combinatorics by : V. Kaimanovich

Download or read book Representation Theory, Dynamical Systems, and Asymptotic Combinatorics written by V. Kaimanovich and published by . This book was released on 2011 with total page 258 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume, devoted to the 70th birthday of the well-known St. Petersburg mathematician A.M. Vershik, contains a collection of articles by participants in the conference "Representation Theory, Dynamical Systems, and Asymptotic Combinatorics", held in St. Petersburg in June of 2004. The book is suitable for graduate students and researchers interested in combinatorial and dynamical aspects of group representation theory.

Computation and Combinatorics in Dynamics, Stochastics and Control

Author : Elena Celledoni
Publisher : Springer
ISBN 13 : 3030015939
Total Pages : 734 pages
Book Rating : 4.0/5 (3 download)

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Book Synopsis Computation and Combinatorics in Dynamics, Stochastics and Control by : Elena Celledoni

Download or read book Computation and Combinatorics in Dynamics, Stochastics and Control written by Elena Celledoni and published by Springer. This book was released on 2019-01-13 with total page 734 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Abel Symposia volume at hand contains a collection of high-quality articles written by the world’s leading experts, and addressing all mathematicians interested in advances in deterministic and stochastic dynamical systems, numerical analysis, and control theory. In recent years we have witnessed a remarkable convergence between individual mathematical disciplines that approach deterministic and stochastic dynamical systems from mathematical analysis, computational mathematics and control theoretical perspectives. Breakthrough developments in these fields now provide a common mathematical framework for attacking many different problems related to differential geometry, analysis and algorithms for stochastic and deterministic dynamics. In the Abel Symposium 2016, which took place from August 16-19 in Rosendal near Bergen, leading researchers in the fields of deterministic and stochastic differential equations, control theory, numerical analysis, algebra and random processes presented and discussed the current state of the art in these diverse fields. The current Abel Symposia volume may serve as a point of departure for exploring these related but diverse fields of research, as well as an indicator of important current and future developments in modern mathematics.

Combinatorics, Words and Symbolic Dynamics

Author : Valérie Berthé
Publisher : Cambridge University Press
ISBN 13 : 1316462528
Total Pages : pages
Book Rating : 4.3/5 (164 download)

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Book Synopsis Combinatorics, Words and Symbolic Dynamics by : Valérie Berthé

Download or read book Combinatorics, Words and Symbolic Dynamics written by Valérie Berthé and published by Cambridge University Press. This book was released on 2016-02-26 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Internationally recognised researchers look at developing trends in combinatorics with applications in the study of words and in symbolic dynamics. They explain the important concepts, providing a clear exposition of some recent results, and emphasise the emerging connections between these different fields. Topics include combinatorics on words, pattern avoidance, graph theory, tilings and theory of computation, multidimensional subshifts, discrete dynamical systems, ergodic theory, numeration systems, dynamical arithmetics, automata theory and synchronised words, analytic combinatorics, continued fractions and probabilistic models. Each topic is presented in a way that links it to the main themes, but then they are also extended to repetitions in words, similarity relations, cellular automata, friezes and Dynkin diagrams. The book will appeal to graduate students, research mathematicians and computer scientists working in combinatorics, theory of computation, number theory, symbolic dynamics, tilings and stringology. It will also interest biologists using text algorithms.

Combinatorics, Words and Symbolic Dynamics

Author : Valérie Berthé
Publisher : Cambridge University Press
ISBN 13 : 1107077028
Total Pages : 496 pages
Book Rating : 4.1/5 (7 download)

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Book Synopsis Combinatorics, Words and Symbolic Dynamics by : Valérie Berthé

Dynamical System Synchronization

Author : Albert C. J. Luo
Publisher : Springer Science & Business Media
ISBN 13 : 1461450977
Total Pages : 245 pages
Book Rating : 4.4/5 (614 download)

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Book Synopsis Dynamical System Synchronization by : Albert C. J. Luo

Download or read book Dynamical System Synchronization written by Albert C. J. Luo and published by Springer Science & Business Media. This book was released on 2013-03-22 with total page 245 pages. Available in PDF, EPUB and Kindle. Book excerpt: Dynamical System Synchronization (DSS) meticulously presents for the first time the theory of dynamical systems synchronization based on the local singularity theory of discontinuous dynamical systems. The book details the sufficient and necessary conditions for dynamical systems synchronizations, through extensive mathematical expression. Techniques for engineering implementation of DSS are clearly presented compared with the existing techniques.