Six Lectures On Dynamical Systems

Author : Bernd Aulbach,Fritz Colonius
Publisher : World Scientific
Page : 332 pages
File Size : 53,9 Mb
Release : 1996
Category : Mathematics
ISBN : 9810225482

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Six Lectures on Dynamical Systems by Bernd Aulbach,Fritz Colonius Pdf

This volume consists of six articles covering different facets of the mathematical theory of dynamical systems. The topics range from topological foundations through invariant manifolds, decoupling, perturbations and computations to control theory. All contributions are based on a sound mathematical analysis. Some of them provide detailed proofs while others are of a survey character. In any case, emphasis is put on motivation and guiding ideas. Many examples are included.The papers of this volume grew out of a tutorial workshop for graduate students in mathematics held at the University of Augsburg. Each of the contributions is self-contained and provides an in-depth insight into some topic of current interest in the mathematical theory of dynamical systems. The text is suitable for courses and seminars on a graduate student level.

Author : B Aulbach,F Colonius
Publisher : World Scientific
Page : 324 pages
File Size : 50,7 Mb
Release : 1996-05-15
Category : Mathematics
ISBN : 9789814499422

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Six Lectures on Dynamical Systems by B Aulbach,F Colonius Pdf

This volume consists of six articles covering different facets of the mathematical theory of dynamical systems. The topics range from topological foundations through invariant manifolds, decoupling, perturbations and computations to control theory. All contributions are based on a sound mathematical analysis. Some of them provide detailed proofs while others are of a survey character. In any case, emphasis is put on motivation and guiding ideas. Many examples are included. The papers of this volume grew out of a tutorial workshop for graduate students in mathematics held at the University of Augsburg. Each of the contributions is self-contained and provides an in-depth insight into some topic of current interest in the mathematical theory of dynamical systems. The text is suitable for courses and seminars on a graduate student level. Contents:Dynamical Systems: The Topological Foundations (E Akin)Integral Manifolds for Carathéodory Type Differential Equations in Banach Spaces (B Aulbach & T Wanner)Control Theory and Dynamical Systems (F Colonius & W Kliemann)Shadowing in Discrete Dynamical Systems (B A Coomes, H Koçak & K J Palmer)Perturbation of Invariant Manifolds of Ordinary Differential Equations (G Osipenko & E Ershov)The Reduction of Discrete Dynamical and Semidynamical Systems in Metric Spaces (A Reinfelds) Readership: Research mathematicians, graduate students in pure and applied mathematics and readers from applied sciences and engineering. keywords:Workshop;Dynamical Systems;Augsburg (Germany);Lectures

Author : Martin Rasmussen
Publisher : Springer
Page : 217 pages
File Size : 49,8 Mb
Release : 2007-05-26
Category : Mathematics
ISBN : 9783540712251

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Attractivity and Bifurcation for Nonautonomous Dynamical Systems by Martin Rasmussen Pdf

Although, bifurcation theory of equations with autonomous and periodic time dependence is a major object of research in the study of dynamical systems since decades, the notion of a nonautonomous bifurcation is not yet established. In this book, two different approaches are developed which are based on special definitions of local attractivity and repulsivity. It is shown that these notions lead to nonautonomous Morse decompositions.

Author : Peter E. Kloeden,Martin Rasmussen
Publisher : American Mathematical Soc.
Page : 274 pages
File Size : 40,8 Mb
Release : 2011-08-17
Category : Mathematics
ISBN : 9780821868713

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Nonautonomous Dynamical Systems by Peter E. Kloeden,Martin Rasmussen Pdf

The theory of nonautonomous dynamical systems in both of its formulations as processes and skew product flows is developed systematically in this book. The focus is on dissipative systems and nonautonomous attractors, in particular the recently introduced concept of pullback attractors. Linearization theory, invariant manifolds, Lyapunov functions, Morse decompositions and bifurcations for nonautonomous systems and set-valued generalizations are also considered as well as applications to numerical approximations, switching systems and synchronization. Parallels with corresponding theories of control and random dynamical systems are briefly sketched. With its clear and systematic exposition, many examples and exercises, as well as its interesting applications, this book can serve as a text at the beginning graduate level. It is also useful for those who wish to begin their own independent research in this rapidly developing area.

Author : Ludwig Arnold
Publisher : Springer Science & Business Media
Page : 590 pages
File Size : 43,9 Mb
Release : 2013-04-17
Category : Mathematics
ISBN : 9783662128787

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Random Dynamical Systems by Ludwig Arnold Pdf

The first systematic presentation of the theory of dynamical systems under the influence of randomness, this book includes products of random mappings as well as random and stochastic differential equations. The basic multiplicative ergodic theorem is presented, providing a random substitute for linear algebra. On its basis, many applications are detailed. Numerous instructive examples are treated analytically or numerically.

Author : George Osipenko
Publisher : Springer
Page : 286 pages
File Size : 53,8 Mb
Release : 2006-10-28
Category : Mathematics
ISBN : 9783540355953

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Dynamical Systems, Graphs, and Algorithms by George Osipenko Pdf

This book describes a family of algorithms for studying the global structure of systems. By a finite covering of the phase space we construct a directed graph with vertices corresponding to cells of the covering and edges corresponding to admissible transitions. The method is used, among other things, to locate the periodic orbits and the chain recurrent set, to construct the attractors and their basins, to estimate the entropy, and more.

Author : Valentin Senderovich Afraĭmovich,Sze-Bi Hsu
Publisher : American Mathematical Soc.
Page : 367 pages
File Size : 44,9 Mb
Release : 2003
Category : Chaotic behavior in systems
ISBN : 9780821831687

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Lectures on Chaotic Dynamical Systems by Valentin Senderovich Afraĭmovich,Sze-Bi Hsu Pdf

Basic concepts Zero-dimensional dynamics One-dimensional dynamics Two-dimensional dynamics Systems with 1.5 degrees of freedom Systems generated by three-dimensional vector fields Lyapunov exponents Appendix Bibliography Index.

Author : Ludwig Arnold,Christopher K.R.T. Jones,Konstantin Mischaikow,Genevieve Raugel
Publisher : Springer
Page : 336 pages
File Size : 53,5 Mb
Release : 2006-11-14
Category : Mathematics
ISBN : 9783540494157

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Dynamical Systems by Ludwig Arnold,Christopher K.R.T. Jones,Konstantin Mischaikow,Genevieve Raugel Pdf

This volume contains the lecture notes written by the four principal speakers at the C.I.M.E. session on Dynamical Systems held at Montecatini, Italy in June 1994. The goal of the session was to illustrate how methods of dynamical systems can be applied to the study of ordinary and partial differential equations. Topics in random differential equations, singular perturbations, the Conley index theory, and non-linear PDEs were discussed. Readers interested in asymptotic behavior of solutions of ODEs and PDEs and familiar with basic notions of dynamical systems will wish to consult this text.

Author : Robert A. Meyers
Publisher : Springer Science & Business Media
Page : 1885 pages
File Size : 44,7 Mb
Release : 2011-10-05
Category : Mathematics
ISBN : 9781461418054

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Mathematics of Complexity and Dynamical Systems by Robert A. Meyers Pdf

Mathematics of Complexity and Dynamical Systems is an authoritative reference to the basic tools and concepts of complexity, systems theory, and dynamical systems from the perspective of pure and applied mathematics. Complex systems are systems that comprise many interacting parts with the ability to generate a new quality of collective behavior through self-organization, e.g. the spontaneous formation of temporal, spatial or functional structures. These systems are often characterized by extreme sensitivity to initial conditions as well as emergent behavior that are not readily predictable or even completely deterministic. The more than 100 entries in this wide-ranging, single source work provide a comprehensive explication of the theory and applications of mathematical complexity, covering ergodic theory, fractals and multifractals, dynamical systems, perturbation theory, solitons, systems and control theory, and related topics. Mathematics of Complexity and Dynamical Systems is an essential reference for all those interested in mathematical complexity, from undergraduate and graduate students up through professional researchers.

Author : Sergei Yu. Pilyugin
Publisher : Springer
Page : 284 pages
File Size : 46,5 Mb
Release : 2006-11-14
Category : Mathematics
ISBN : 9783540484295

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Shadowing in Dynamical Systems by Sergei Yu. Pilyugin Pdf

This book is an introduction to the theory of shadowing of approximate trajectories in dynamical systems by exact ones. This is the first book completely devoted to the theory of shadowing. It shows the importance of shadowing theory for both the qualitative theory of dynamical systems and the theory of numerical methods. Shadowing Methods allow us to estimate differences between exact and approximate solutions on infinite time intervals and to understand the influence of error terms. The book is intended for specialists in dynamical systems, for researchers and graduate students in the theory of numerical methods.

Author : Ethan Akin
Publisher : American Mathematical Soc.
Page : 197 pages
File Size : 41,9 Mb
Release : 1999
Category : Mathematics
ISBN : 9780821813836

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Simplicial Dynamical Systems by Ethan Akin Pdf

Abstract A - simplicial dynamical system is a simplicial map $g:K^* \rightarrow K$ where $K$ is a finite simplicial complex triangulating a compact polyhedron $X$ and $K^*$ is a proper subdivision of $K$, e.g. the barycentric or any further subdivision. The dynamics of the associated piecewise linear map $g: X X$ can be analyzed by using certain naturally related subshifts of finite type. Any continuous map on $X$ can be $C^0$ approximated by such systems. Other examples yield interesting subshift constructions.

Author : James A. Yorke
Publisher : Springer
Page : 282 pages
File Size : 41,6 Mb
Release : 2006-11-15
Category : Mathematics
ISBN : 9783540363064

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Seminar on Differential Equations and Dynamical Systems by James A. Yorke Pdf

Author : Evgenij B. Dynkin
Publisher : American Mathematical Soc.
Page : 92 pages
File Size : 47,9 Mb
Release : 1963-12-31
Category : Electronic
ISBN : 082189613X

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Six lectures delivered at the International Congress of Mathematicians in Stockholm, 1962 by Evgenij B. Dynkin Pdf

Author : Nguyen Dinh Cong
Publisher : Oxford University Press
Page : 216 pages
File Size : 47,8 Mb
Release : 1997
Category : Mathematics
ISBN : 0198501579

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Topological Dynamics of Random Dynamical Systems by Nguyen Dinh Cong Pdf

This book is the first systematic treatment of the theory of topological dynamics of random dynamical systems. A relatively new field, the theory of random dynamical systems unites and develops the classical deterministic theory of dynamical systems and probability theory, finding numerous applications in disciplines ranging from physics and biology to engineering, finance and economics. This book presents in detail the solutions to the most fundamental problems of topological dynamics: linearization of nonlinear smooth systems, classification, and structural stability of linear hyperbolic systems. Employing the tools and methods of algebraic ergodic theory, the theory presented in the book has surprisingly beautiful results showing the richness of random dynamical systems as well as giving a gentle generalization of the classical deterministic theory.

Author : Christoph Kawan
Publisher : Springer
Page : 290 pages
File Size : 49,6 Mb
Release : 2013-10-02
Category : Mathematics
ISBN : 9783319012889

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Invariance Entropy for Deterministic Control Systems by Christoph Kawan Pdf

This monograph provides an introduction to the concept of invariance entropy, the central motivation of which lies in the need to deal with communication constraints in networked control systems. For the simplest possible network topology, consisting of one controller and one dynamical system connected by a digital channel, invariance entropy provides a measure for the smallest data rate above which it is possible to render a given subset of the state space invariant by means of a symbolic coder-controller pair. This concept is essentially equivalent to the notion of topological feedback entropy introduced by Nair, Evans, Mareels and Moran (Topological feedback entropy and nonlinear stabilization. IEEE Trans. Automat. Control 49 (2004), 1585–1597). The book presents the foundations of a theory which aims at finding expressions for invariance entropy in terms of dynamical quantities such as Lyapunov exponents. While both discrete-time and continuous-time systems are treated, the emphasis lies on systems given by differential equations.