Chaos Fractals And Noise Stochastic Aspects Of Dynamics

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Chaos, Fractals, and Noise

Author : Andrzej Lasota
Publisher : New York : Springer-Verlag
ISBN 13 :
Total Pages : 496 pages
Book Rating : 4.:/5 (318 download)

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Book Synopsis Chaos, Fractals, and Noise by : Andrzej Lasota

Download or read book Chaos, Fractals, and Noise written by Andrzej Lasota and published by New York : Springer-Verlag. This book was released on 1994 with total page 496 pages. Available in PDF, EPUB and Kindle. Book excerpt: In recent years there has been an explosive growth in the study of physical, biological, and economic systems that can be profitably studied using densities. Because of the general inaccessibility of the mathematical literature to the nonspecialist, little diffusion of the applicable mathematics into the study of these "chaotic" systems has taken place. This book will help bridge that gap. To show how densities arise in simple deterministic systems, the authors give a unified treatment of a variety of mathematical systems generating densities, ranging from one-dimensional discrete time transformations through continuous time systems described by integro-partial-differential equations. Examples have been drawn from many fields to illustrate the utility of the concepts and techniques presented, and the ideas in this book should thus prove useful in the study of a number of applied sciences. The authors assume that the reader has a knowledge of advanced calculus and differential equations. Basic concepts from measure theory, ergodic theory, the geometry of manifolds, partial differential equations, probability theory and Markov processes, and stochastic integrals and differential equations are introduced as needed. Physicists, chemists, and biomathematicians studying chaotic behavior will find this book of value. It will also be a useful reference or text for mathematicians and graduate students working in ergodic theory and dynamical systems.

Dynamics of Dissipation

Author : Piotr Garbaczewski
Publisher : Springer Science & Business Media
ISBN 13 : 3540461221
Total Pages : 516 pages
Book Rating : 4.5/5 (44 download)

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Book Synopsis Dynamics of Dissipation by : Piotr Garbaczewski

Download or read book Dynamics of Dissipation written by Piotr Garbaczewski and published by Springer Science & Business Media. This book was released on 2007-08-04 with total page 516 pages. Available in PDF, EPUB and Kindle. Book excerpt: This collection of lectures treats the dynamics of open systems with a strong emphasis on dissipation phenomena related to dynamical chaos. This research area is very broad, covering topics such as nonequilibrium statistical mechanics, environment-system coupling (decoherence) and applications of Markov semi-groups to name but a few. The book addresses not only experienced researchers in the field but also nonspecialists from related areas of research, postgraduate students wishing to enter the field and lecturers searching for advanced textbook material.

Chaos, Noise and Fractals

Author : E. Roy Pike
Publisher : CRC Press
ISBN 13 : 9780852743645
Total Pages : 282 pages
Book Rating : 4.7/5 (436 download)

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Book Synopsis Chaos, Noise and Fractals by : E. Roy Pike

Download or read book Chaos, Noise and Fractals written by E. Roy Pike and published by CRC Press. This book was released on 1987-01-01 with total page 282 pages. Available in PDF, EPUB and Kindle. Book excerpt: The study of nonlinear dynamical systems has been gathering momentum since the late 1950s. It now constitutes one of the major research areas of modern theoretical physics. The twin themes of fractals and chaos, which are linked by attracting sets in chaotic systems that are fractal in structure, are currently generating a great deal of excitement. The degree of structure robustness in the presence of stochastic and quantum noise is thus a topic of interest. Chaos, Noise and Fractals discusses the role of fractals in quantum mechanics, the influence of phase noise in chaos and driven optical systems, and the arithmetic of chaos. The book represents a balanced overview of the field and is a worthy addition to the reading lists of researchers and students interested in any of the varied, and sometimes bizarre, aspects of this intriguing subject.

Nonlinear Dynamics and Chaos

Author : Steven H. Strogatz
Publisher : CRC Press
ISBN 13 : 0429961111
Total Pages : 532 pages
Book Rating : 4.4/5 (299 download)

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Book Synopsis Nonlinear Dynamics and Chaos by : Steven H. Strogatz

Download or read book Nonlinear Dynamics and Chaos written by Steven H. Strogatz and published by CRC Press. This book was released on 2018-05-04 with total page 532 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook is aimed at newcomers to nonlinear dynamics and chaos, especially students taking a first course in the subject. The presentation stresses analytical methods, concrete examples, and geometric intuition. The theory is developed systematically, starting with first-order differential equations and their bifurcations, followed by phase plane analysis, limit cycles and their bifurcations, and culminating with the Lorenz equations, chaos, iterated maps, period doubling, renormalization, fractals, and strange attractors.

Advances in Dynamics, Optimization and Computation

Author : Oliver Junge
Publisher : Springer Nature
ISBN 13 : 3030512649
Total Pages : 402 pages
Book Rating : 4.0/5 (35 download)

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Book Synopsis Advances in Dynamics, Optimization and Computation by : Oliver Junge

Download or read book Advances in Dynamics, Optimization and Computation written by Oliver Junge and published by Springer Nature. This book was released on 2020-07-20 with total page 402 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a collection of papers on recent advances in problems concerning dynamics, optimal control and optimization. In many chapters, computational techniques play a central role. Set-oriented techniques feature prominently throughout the book, yielding state-of-the-art algorithms for computing general invariant sets, constructing globally optimal controllers and solving multi-objective optimization problems.

Abstract Compositional Analysis of Iterated Relations

Author : Frederic Geurts
Publisher : Springer
ISBN 13 : 3540492119
Total Pages : 283 pages
Book Rating : 4.5/5 (44 download)

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Book Synopsis Abstract Compositional Analysis of Iterated Relations by : Frederic Geurts

Download or read book Abstract Compositional Analysis of Iterated Relations written by Frederic Geurts and published by Springer. This book was released on 2003-06-26 with total page 283 pages. Available in PDF, EPUB and Kindle. Book excerpt: This self-contained monograph is an integrated study of generic systems defined by iterated relations using the two paradigms of abstraction and composition. This accommodates the complexity of some state-transition systems and improves understanding of complex or chaotic phenomena emerging in some dynamical systems. The main insights and results of this work concern a structural form of complexity obtained by composition of simple interacting systems representing opposed attracting behaviors. This complexity is expressed in the evolution of composed systems (their dynamics) and in the relations between their initial and final states (the computation they realize). The theoretical results are validated by analyzing dynamical and computational properties of low-dimensional prototypes of chaotic systems, high-dimensional spatiotemporally complex systems, and formal systems.

Stochastic Dynamics of Structures

Author : Jie Li
Publisher : John Wiley & Sons
ISBN 13 : 0470824247
Total Pages : 435 pages
Book Rating : 4.4/5 (78 download)

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Book Synopsis Stochastic Dynamics of Structures by : Jie Li

Download or read book Stochastic Dynamics of Structures written by Jie Li and published by John Wiley & Sons. This book was released on 2009-09-28 with total page 435 pages. Available in PDF, EPUB and Kindle. Book excerpt: In Stochastic Dynamics of Structures, Li and Chen present a unified view of the theory and techniques for stochastic dynamics analysis, prediction of reliability, and system control of structures within the innovative theoretical framework of physical stochastic systems. The authors outline the fundamental concepts of random variables, stochastic process and random field, and orthogonal expansion of random functions. Readers will gain insight into core concepts such as stochastic process models for typical dynamic excitations of structures, stochastic finite element, and random vibration analysis. Li and Chen also cover advanced topics, including the theory of and elaborate numerical methods for probability density evolution analysis of stochastic dynamical systems, reliability-based design, and performance control of structures. Stochastic Dynamics of Structures presents techniques for researchers and graduate students in a wide variety of engineering fields: civil engineering, mechanical engineering, aerospace and aeronautics, marine and offshore engineering, ship engineering, and applied mechanics. Practicing engineers will benefit from the concise review of random vibration theory and the new methods introduced in the later chapters. "The book is a valuable contribution to the continuing development of the field of stochastic structural dynamics, including the recent discoveries and developments by the authors of the probability density evolution method (PDEM) and its applications to the assessment of the dynamic reliability and control of complex structures through the equivalent extreme-value distribution." —A. H-S. Ang, NAE, Hon. Mem. ASCE, Research Professor, University of California, Irvine, USA "The authors have made a concerted effort to present a responsible and even holistic account of modern stochastic dynamics. Beyond the traditional concepts, they also discuss theoretical tools of recent currency such as the Karhunen-Loeve expansion, evolutionary power spectra, etc. The theoretical developments are properly supplemented by examples from earthquake, wind, and ocean engineering. The book is integrated by also comprising several useful appendices, and an exhaustive list of references; it will be an indispensable tool for students, researchers, and practitioners endeavoring in its thematic field." —Pol Spanos, NAE, Ryon Chair in Engineering, Rice University, Houston, USA

Normally Hyperbolic Invariant Manifolds in Dynamical Systems

Author : Stephen Wiggins
Publisher : Springer Science & Business Media
ISBN 13 : 1461243122
Total Pages : 198 pages
Book Rating : 4.4/5 (612 download)

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Book Synopsis Normally Hyperbolic Invariant Manifolds in Dynamical Systems by : Stephen Wiggins

Download or read book Normally Hyperbolic Invariant Manifolds in Dynamical Systems written by Stephen Wiggins and published by Springer Science & Business Media. This book was released on 2013-11-22 with total page 198 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the past ten years, there has been much progress in understanding the global dynamics of systems with several degrees-of-freedom. An important tool in these studies has been the theory of normally hyperbolic invariant manifolds and foliations of normally hyperbolic invariant manifolds. In recent years these techniques have been used for the development of global perturbation methods, the study of resonance phenomena in coupled oscillators, geometric singular perturbation theory, and the study of bursting phenomena in biological oscillators. "Invariant manifold theorems" have become standard tools for applied mathematicians, physicists, engineers, and virtually anyone working on nonlinear problems from a geometric viewpoint. In this book, the author gives a self-contained development of these ideas as well as proofs of the main theorems along the lines of the seminal works of Fenichel. In general, the Fenichel theory is very valuable for many applications, but it is not easy for people to get into from existing literature. This book provides an excellent avenue to that. Wiggins also describes a variety of settings where these techniques can be used in applications.

An Introduction to the Mathematical Theory of Inverse Problems

Author : Andreas Kirsch
Publisher : Springer Science & Business Media
ISBN 13 : 9780387945309
Total Pages : 304 pages
Book Rating : 4.9/5 (453 download)

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Book Synopsis An Introduction to the Mathematical Theory of Inverse Problems by : Andreas Kirsch

Download or read book An Introduction to the Mathematical Theory of Inverse Problems written by Andreas Kirsch and published by Springer Science & Business Media. This book was released on 1996-09-26 with total page 304 pages. Available in PDF, EPUB and Kindle. Book excerpt: Following Keller [119] we call two problems inverse to each other if the for mulation of each of them requires full or partial knowledge of the other. By this definition, it is obviously arbitrary which of the two problems we call the direct and which we call the inverse problem. But usually, one of the problems has been studied earlier and, perhaps, in more detail. This one is usually called the direct problem, whereas the other is the inverse problem. However, there is often another, more important difference between these two problems. Hadamard (see [91]) introduced the concept of a well-posed problem, originating from the philosophy that the mathematical model of a physical problem has to have the properties of uniqueness, existence, and stability of the solution. If one of the properties fails to hold, he called the problem ill-posed. It turns out that many interesting and important inverse in science lead to ill-posed problems, while the corresponding di problems rect problems are well-posed. Often, existence and uniqueness can be forced by enlarging or reducing the solution space (the space of "models"). For restoring stability, however, one has to change the topology of the spaces, which is in many cases impossible because of the presence of measurement errors. At first glance, it seems to be impossible to compute the solution of a problem numerically if the solution of the problem does not depend continuously on the data, i. e. , for the case of ill-posed problems.

Theory and Applications of Partial Functional Differential Equations

Author : Jianhong Wu
Publisher : Springer Science & Business Media
ISBN 13 : 1461240506
Total Pages : 441 pages
Book Rating : 4.4/5 (612 download)

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Book Synopsis Theory and Applications of Partial Functional Differential Equations by : Jianhong Wu

Download or read book Theory and Applications of Partial Functional Differential Equations written by Jianhong Wu and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 441 pages. Available in PDF, EPUB and Kindle. Book excerpt: Abstract semilinear functional differential equations arise from many biological, chemical, and physical systems which are characterized by both spatial and temporal variables and exhibit various spatio-temporal patterns. The aim of this book is to provide an introduction of the qualitative theory and applications of these equations from the dynamical systems point of view. The required prerequisites for that book are at a level of a graduate student. The style of presentation will be appealing to people trained and interested in qualitative theory of ordinary and functional differential equations.

Theory of Multicomponent Fluids

Author : Donald A. Drew
Publisher : Springer Science & Business Media
ISBN 13 : 0387226370
Total Pages : 311 pages
Book Rating : 4.3/5 (872 download)

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Book Synopsis Theory of Multicomponent Fluids by : Donald A. Drew

Download or read book Theory of Multicomponent Fluids written by Donald A. Drew and published by Springer Science & Business Media. This book was released on 2006-05-10 with total page 311 pages. Available in PDF, EPUB and Kindle. Book excerpt: An exposition of the derivation and use of equations of motion for two-phase flow. The approach taken derives the equations of motion using ensemble averaging, and compares them with those derived from control volume methods. Closure for dispersed flows is discussed, and some fundamental solutions are given. The work focuses on the fundamental aspects of two-phase flow, and is intended to give the reader a background for understanding the dynamics as well as a system of equations that can be used in predictions of the behavior of dispersed two-phase flows. The exposition in terms of ensemble averaging is new, and combining it with modern continuum mechanics concepts makes this book unique. Intended for engineering, mathematics and physics researchers and advanced graduate students working in the field.

Nonlinear Theory of Shallow Shells

Author : Iosif I. Vorovich
Publisher : Springer Science & Business Media
ISBN 13 : 0387227768
Total Pages : 404 pages
Book Rating : 4.3/5 (872 download)

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Book Synopsis Nonlinear Theory of Shallow Shells by : Iosif I. Vorovich

Download or read book Nonlinear Theory of Shallow Shells written by Iosif I. Vorovich and published by Springer Science & Business Media. This book was released on 2008-01-08 with total page 404 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents rigorous treatment of boundary value problems in nonlinear theory of shallow shells. The consideration of the problems is carried out using methods of nonlinear functional analysis.

Introduction to Spectral Theory

Author : P.D. Hislop
Publisher : Springer Science & Business Media
ISBN 13 : 146120741X
Total Pages : 331 pages
Book Rating : 4.4/5 (612 download)

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Book Synopsis Introduction to Spectral Theory by : P.D. Hislop

Download or read book Introduction to Spectral Theory written by P.D. Hislop and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 331 pages. Available in PDF, EPUB and Kindle. Book excerpt: The intention of this book is to introduce students to active areas of research in mathematical physics in a rather direct way minimizing the use of abstract mathematics. The main features are geometric methods in spectral analysis, exponential decay of eigenfunctions, semi-classical analysis of bound state problems, and semi-classical analysis of resonance. A new geometric point of view along with new techniques are brought out in this book which have both been discovered within the past decade. This book is designed to be used as a textbook, unlike the competitors which are either too fundamental in their approach or are too abstract in nature to be considered as texts. The authors' text fills a gap in the marketplace.

Singularities and Groups in Bifurcation Theory

Author : Martin Golubitsky
Publisher : Springer Science & Business Media
ISBN 13 : 146125034X
Total Pages : 480 pages
Book Rating : 4.4/5 (612 download)

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Book Synopsis Singularities and Groups in Bifurcation Theory by : Martin Golubitsky

Download or read book Singularities and Groups in Bifurcation Theory written by Martin Golubitsky and published by Springer Science & Business Media. This book was released on 2013-11-27 with total page 480 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book has been written in a frankly partisian spirit-we believe that singularity theory offers an extremely useful approach to bifurcation prob lems and we hope to convert the reader to this view. In this preface we will discuss what we feel are the strengths of the singularity theory approach. This discussion then Ieads naturally into a discussion of the contents of the book and the prerequisites for reading it. Let us emphasize that our principal contribution in this area has been to apply pre-existing techniques from singularity theory, especially unfolding theory and classification theory, to bifurcation problems. Many ofthe ideas in this part of singularity theory were originally proposed by Rene Thom; the subject was then developed rigorously by John Matherand extended by V. I. Arnold. In applying this material to bifurcation problems, we were greatly encouraged by how weil the mathematical ideas of singularity theory meshed with the questions addressed by bifurcation theory. Concerning our title, Singularities and Groups in Bifurcation Theory, it should be mentioned that the present text is the first volume in a two-volume sequence. In this volume our emphasis is on singularity theory, with group theory playing a subordinate role. In Volume II the emphasis will be more balanced. Having made these remarks, Iet us set the context for the discussion of the strengths of the singularity theory approach to bifurcation. As we use the term, bifurcation theory is the study of equations with multiple solutions.

Inverse Acoustic and Electromagnetic Scattering Theory

Author : David Colton
Publisher : Springer Science & Business Media
ISBN 13 : 3662035375
Total Pages : 347 pages
Book Rating : 4.6/5 (62 download)

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Book Synopsis Inverse Acoustic and Electromagnetic Scattering Theory by : David Colton

Download or read book Inverse Acoustic and Electromagnetic Scattering Theory written by David Colton and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 347 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is devoted to the mathematical and numerical analysis of the inverse scattering problem for acoustic and electromagnetic waves. The second edition includes material on Newton’s method for the inverse obstacle problem, an elegant proof of uniqueness for the inverse medium problem, a discussion of the spectral theory of the far field operator and a method for determining the support of an inhomogeneous medium from far field data.

Linear Operator Theory in Engineering and Science

Author : Arch W. Naylor
Publisher : Springer Science & Business Media
ISBN 13 : 9780387950013
Total Pages : 648 pages
Book Rating : 4.9/5 (5 download)

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Book Synopsis Linear Operator Theory in Engineering and Science by : Arch W. Naylor

Download or read book Linear Operator Theory in Engineering and Science written by Arch W. Naylor and published by Springer Science & Business Media. This book was released on 1982 with total page 648 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a unique introduction to the theory of linear operators on Hilbert space. The authors' goal is to present the basic facts of functional analysis in a form suitable for engineers, scientists, and applied mathematicians. Although the Definition-Theorem-Proof format of mathematics is used, careful attention is given to motivation of the material covered and many illustrative examples are presented. First published in 1971, Linear Operator in Engineering and Sciences has since proved to be a popular and very useful textbook.

Fundamentals of the New Artificial Intelligence

Author : Toshinori Munakata
Publisher : Springer Science & Business Media
ISBN 13 : 1846288398
Total Pages : 266 pages
Book Rating : 4.8/5 (462 download)

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Book Synopsis Fundamentals of the New Artificial Intelligence by : Toshinori Munakata

Download or read book Fundamentals of the New Artificial Intelligence written by Toshinori Munakata and published by Springer Science & Business Media. This book was released on 2008-01-01 with total page 266 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book covers the most essential and widely employed material in each area, particularly the material important for real-world applications. Our goal is not to cover every latest progress in the fields, nor to discuss every detail of various techniques that have been developed. New sections/subsections added in this edition are: Simulated Annealing (Section 3.7), Boltzmann Machines (Section 3.8) and Extended Fuzzy if-then Rules Tables (Sub-section 5.5.3). Also, numerous changes and typographical corrections have been made throughout the manuscript. The Preface to the first edition follows. General scope of the book Artificial intelligence (AI) as a field has undergone rapid growth in diversification and practicality. For the past few decades, the repertoire of AI techniques has evolved and expanded. Scores of newer fields have been added to the traditional symbolic AI. Symbolic AI covers areas such as knowledge-based systems, logical reasoning, symbolic machine learning, search techniques, and natural language processing. The newer fields include neural networks, genetic algorithms or evolutionary computing, fuzzy systems, rough set theory, and chaotic systems.