Shadowing In Dynamical Systems

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Shadowing in Dynamical Systems

Author : Sergei Yu. Pilyugin
Publisher : Springer
ISBN 13 : 3540484299
Total Pages : 284 pages
Book Rating : 4.5/5 (44 download)

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Book Synopsis Shadowing in Dynamical Systems by : Sergei Yu. Pilyugin

Download or read book Shadowing in Dynamical Systems written by Sergei Yu. Pilyugin and published by Springer. This book was released on 2006-11-14 with total page 284 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Shadowing in Dynamical Systems

Author : K.J. Palmer
Publisher : Springer Science & Business Media
ISBN 13 : 1475732104
Total Pages : 307 pages
Book Rating : 4.4/5 (757 download)

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Book Synopsis Shadowing in Dynamical Systems by : K.J. Palmer

Download or read book Shadowing in Dynamical Systems written by K.J. Palmer and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 307 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this book the theory of hyperbolic sets is developed, both for diffeomorphisms and flows, with an emphasis on shadowing. We show that hyperbolic sets are expansive and have the shadowing property. Then we use shadowing to prove that hyperbolic sets are robust under perturbation, that they have an asymptotic phase property and also that the dynamics near a transversal homoclinic orbit is chaotic. It turns out that chaotic dynamical systems arising in practice are not quite hyperbolic. However, they possess enough hyperbolicity to enable us to use shadowing ideas to give computer-assisted proofs that computed orbits of such systems can be shadowed by true orbits for long periods of time, that they possess periodic orbits of long periods and that it is really true that they are chaotic. Audience: This book is intended primarily for research workers in dynamical systems but could also be used in an advanced graduate course taken by students familiar with calculus in Banach spaces and with the basic existence theory for ordinary differential equations.

Six Lectures on Dynamical Systems

Author : Bernd Aulbach
Publisher : World Scientific
ISBN 13 : 9789810225483
Total Pages : 332 pages
Book Rating : 4.2/5 (254 download)

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Book Synopsis Six Lectures on Dynamical Systems by : Bernd Aulbach

Download or read book Six Lectures on Dynamical Systems written by Bernd Aulbach and published by World Scientific. This book was released on 1996 with total page 332 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Spaces of Dynamical Systems

Author : Sergei Yu. Pilyugin
Publisher : Walter de Gruyter GmbH & Co KG
ISBN 13 : 3110653990
Total Pages : 351 pages
Book Rating : 4.1/5 (16 download)

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Book Synopsis Spaces of Dynamical Systems by : Sergei Yu. Pilyugin

Download or read book Spaces of Dynamical Systems written by Sergei Yu. Pilyugin and published by Walter de Gruyter GmbH & Co KG. This book was released on 2019-08-05 with total page 351 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Recent Trends In Chaotic, Nonlinear And Complex Dynamics

Author : Jan Awrejcewicz
Publisher : World Scientific
ISBN 13 : 981122191X
Total Pages : 561 pages
Book Rating : 4.8/5 (112 download)

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Book Synopsis Recent Trends In Chaotic, Nonlinear And Complex Dynamics by : Jan Awrejcewicz

Download or read book Recent Trends In Chaotic, Nonlinear And Complex Dynamics written by Jan Awrejcewicz and published by World Scientific. This book was released on 2021-07-26 with total page 561 pages. Available in PDF, EPUB and Kindle. Book excerpt: In recent years, enormous progress has been made on nonlinear dynamics particularly on chaos and complex phenomena. This unique volume presents the advances made in theory, analysis, numerical simulation and experimental realization, promising novel practical applications on various topics of current interest on chaos and related fields of nonlinear dynamics.Particularly, the focus is on the following topics: synchronization vs. chaotic phenomena, chaos and its control in engineering dynamical systems, fractal-based dynamics, uncertainty and unpredictability measures vs. chaos, Hamiltonian systems and systems with time delay, local/global stability, bifurcations and their control, applications of machine learning to chaos, nonlinear vibrations of lumped mass mechanical/mechatronic systems (rigid body and coupled oscillator dynamics) governed by ODEs and continuous structural members (beams, plates, shells) vibrations governed by PDEs, patterns formation, chaos in micro- and nano-mechanical systems, chaotic reduced-order models, energy absorption/harvesting from chaotic, chaos vs. resonance phenomena, chaos exhibited by discontinuous systems, chaos in lab experiments.The present volume forms an invaluable source on recent trends in chaotic and complex dynamics for any researcher and newcomers to the field of nonlinear dynamics.

Differentiable Dynamical Systems

Author : Lan Wen
Publisher : American Mathematical Soc.
ISBN 13 : 1470427990
Total Pages : 207 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Differentiable Dynamical Systems by : Lan Wen

Download or read book Differentiable Dynamical Systems written by Lan Wen and published by American Mathematical Soc.. This book was released on 2016-07-20 with total page 207 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a graduate text in differentiable dynamical systems. It focuses on structural stability and hyperbolicity, a topic that is central to the field. Starting with the basic concepts of dynamical systems, analyzing the historic systems of the Smale horseshoe, Anosov toral automorphisms, and the solenoid attractor, the book develops the hyperbolic theory first for hyperbolic fixed points and then for general hyperbolic sets. The problems of stable manifolds, structural stability, and shadowing property are investigated, which lead to a highlight of the book, the Ω-stability theorem of Smale. While the content is rather standard, a key objective of the book is to present a thorough treatment for some tough material that has remained an obstacle to teaching and learning the subject matter. The treatment is straightforward and hence could be particularly suitable for self-study. Selected solutions are available electronically for instructors only. Please send email to [email protected] for more information.

Introduction to the Modern Theory of Dynamical Systems

Author : Anatole Katok
Publisher : Cambridge University Press
ISBN 13 : 9780521575577
Total Pages : 828 pages
Book Rating : 4.5/5 (755 download)

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Book Synopsis Introduction to the Modern Theory of Dynamical Systems by : Anatole Katok

Download or read book Introduction to the Modern Theory of Dynamical Systems written by Anatole Katok and published by Cambridge University Press. This book was released on 1995 with total page 828 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provided the first self-contained comprehensive exposition of the theory of dynamical systems as a core mathematical discipline closely intertwined with most of the main areas of mathematics. The authors introduce and rigorously develop the theory while providing researchers interested in applications with fundamental tools and paradigms. The book begins with a discussion of several elementary but fundamental examples. These are used to formulate a program for the general study of asymptotic properties and to introduce the principal theoretical concepts and methods. The main theme of the second part of the book is the interplay between local analysis near individual orbits and the global complexity of the orbit structure. The third and fourth parts develop the theories of low-dimensional dynamical systems and hyperbolic dynamical systems in depth. Over 400 systematic exercises are included in the text. The book is aimed at students and researchers in mathematics at all levels from advanced undergraduate up.

Principles of Discontinuous Dynamical Systems

Author : Marat Akhmet
Publisher : Springer Science & Business Media
ISBN 13 : 1441965815
Total Pages : 185 pages
Book Rating : 4.4/5 (419 download)

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Book Synopsis Principles of Discontinuous Dynamical Systems by : Marat Akhmet

Download or read book Principles of Discontinuous Dynamical Systems written by Marat Akhmet and published by Springer Science & Business Media. This book was released on 2010-08-26 with total page 185 pages. Available in PDF, EPUB and Kindle. Book excerpt: Discontinuous dynamical systems have played an important role in both theory and applications during the last several decades. This is still an area of active research and techniques to make the applications more effective are an ongoing topic of interest. Principles of Discontinuous Dynamical Systems is devoted to the theory of differential equations with variable moments of impulses. It introduces a new strategy of implementing an equivalence to systems whose solutions have prescribed moments of impulses and utilizing special topologies in spaces of piecewise continuous functions. The achievements obtained on the basis of this approach are described in this book. The text progresses systematically, by covering preliminaries in the first four chapters. This is followed by more complex material and special topics such as Hopf bifurcation, Devaney's chaos, and the shadowing property are discussed in the last two chapters. This book is suitable for researchers and graduate students in mathematics and also in diverse areas such as biology, computer science, and engineering who deal with real world problems.

The Space of Dynamical Systems with the C0-topology

Author : Sergei Yurievitch Pilyugin
Publisher : Springer
ISBN 13 :
Total Pages : 212 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis The Space of Dynamical Systems with the C0-topology by : Sergei Yurievitch Pilyugin

Download or read book The Space of Dynamical Systems with the C0-topology written by Sergei Yurievitch Pilyugin and published by Springer. This book was released on 1994 with total page 212 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Topological Theory of Dynamical Systems

Author : N. Aoki
Publisher : Elsevier
ISBN 13 : 008088721X
Total Pages : 425 pages
Book Rating : 4.0/5 (88 download)

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Book Synopsis Topological Theory of Dynamical Systems by : N. Aoki

Download or read book Topological Theory of Dynamical Systems written by N. Aoki and published by Elsevier. This book was released on 1994-06-03 with total page 425 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph aims to provide an advanced account of some aspects of dynamical systems in the framework of general topology, and is intended for use by interested graduate students and working mathematicians. Although some of the topics discussed are relatively new, others are not: this book is not a collection of research papers, but a textbook to present recent developments of the theory that could be the foundations for future developments.This book contains a new theory developed by the authors to deal with problems occurring in diffentiable dynamics that are within the scope of general topology. To follow it, the book provides an adequate foundation for topological theory of dynamical systems, and contains tools which are sufficiently powerful throughout the book.Graduate students (and some undergraduates) with sufficient knowledge of basic general topology, basic topological dynamics, and basic algebraic topology will find little difficulty in reading this book.

Dynamics of Linear Operators

Author : Frédéric Bayart
Publisher : Cambridge University Press
ISBN 13 : 0521514967
Total Pages : 352 pages
Book Rating : 4.5/5 (215 download)

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Book Synopsis Dynamics of Linear Operators by : Frédéric Bayart

Download or read book Dynamics of Linear Operators written by Frédéric Bayart and published by Cambridge University Press. This book was released on 2009-06-04 with total page 352 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first book to assemble the wide body of theory which has rapidly developed on the dynamics of linear operators. Written for researchers in operator theory, but also accessible to anyone with a reasonable background in functional analysis at the graduate level.

Linear Chaos

Author : Karl-G. Grosse-Erdmann
Publisher : Springer Science & Business Media
ISBN 13 : 1447121708
Total Pages : 391 pages
Book Rating : 4.4/5 (471 download)

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Book Synopsis Linear Chaos by : Karl-G. Grosse-Erdmann

Download or read book Linear Chaos written by Karl-G. Grosse-Erdmann and published by Springer Science & Business Media. This book was released on 2011-08-24 with total page 391 pages. Available in PDF, EPUB and Kindle. Book excerpt: It is commonly believed that chaos is linked to non-linearity, however many (even quite natural) linear dynamical systems exhibit chaotic behavior. The study of these systems is a young and remarkably active field of research, which has seen many landmark results over the past two decades. Linear dynamics lies at the crossroads of several areas of mathematics including operator theory, complex analysis, ergodic theory and partial differential equations. At the same time its basic ideas can be easily understood by a wide audience. Written by two renowned specialists, Linear Chaos provides a welcome introduction to this theory. Split into two parts, part I presents a self-contained introduction to the dynamics of linear operators, while part II covers selected, largely independent topics from linear dynamics. More than 350 exercises and many illustrations are included, and each chapter contains a further ‘Sources and Comments’ section. The only prerequisites are a familiarity with metric spaces, the basic theory of Hilbert and Banach spaces and fundamentals of complex analysis. More advanced tools, only needed occasionally, are provided in two appendices. A self-contained exposition, this book will be suitable for self-study and will appeal to advanced undergraduate or beginning graduate students. It will also be of use to researchers in other areas of mathematics such as partial differential equations, dynamical systems and ergodic theory.

The Diophantine Frobenius Problem

Author : Jorge L. Ramírez Alfonsín
Publisher : Oxford University Press, USA
ISBN 13 : 0198568207
Total Pages : 260 pages
Book Rating : 4.1/5 (985 download)

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Book Synopsis The Diophantine Frobenius Problem by : Jorge L. Ramírez Alfonsín

Download or read book The Diophantine Frobenius Problem written by Jorge L. Ramírez Alfonsín and published by Oxford University Press, USA. This book was released on 2005-12 with total page 260 pages. Available in PDF, EPUB and Kindle. Book excerpt: During the early part of the last century, Ferdinand Georg Frobenius (1849-1917) raised he following problem, known as the Frobenius Problem (FP): given relatively prime positive integers a1,...,an, find the largest natural number (called the Frobenius number and denoted by g(a1,...,an) that is not representable as a nonnegative integer combination of a1,...,an, . At first glance FP may look deceptively specialized. Nevertheless it crops up again and again in the most unexpected places and has been extremely useful in investigating many different problems. A number of methods, from several areas of mathematics, have been used in the hope of finding a formula giving the Frobenius number and algorithms to calculate it. The main intention of this book is to highlight such methods, ideas, viewpoints and applications to a broader audience.

Topology And Dynamics Of Chaos: In Celebration Of Robert Gilmore's 70th Birthday

Author : Christophe Letellier
Publisher : World Scientific
ISBN 13 : 9814434876
Total Pages : 362 pages
Book Rating : 4.8/5 (144 download)

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Book Synopsis Topology And Dynamics Of Chaos: In Celebration Of Robert Gilmore's 70th Birthday by : Christophe Letellier

Download or read book Topology And Dynamics Of Chaos: In Celebration Of Robert Gilmore's 70th Birthday written by Christophe Letellier and published by World Scientific. This book was released on 2013-01-11 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 Rössler, René 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 — not necessarily widely known — contributions (about the different types of chaos introduced by Rössler and not just the “Rössler attractor”; Gumowski and Mira's contributions in electronics; Poincaré's heritage in nonlinear dynamics) but also some recent applications in laser dynamics, biology, etc.

Equilibrium States and the Ergodic Theory of Anosov Diffeomorphisms

Author : Robert Edward Bowen
Publisher : Springer
ISBN 13 : 3540776958
Total Pages : 85 pages
Book Rating : 4.5/5 (47 download)

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Book Synopsis Equilibrium States and the Ergodic Theory of Anosov Diffeomorphisms by : Robert Edward Bowen

Download or read book Equilibrium States and the Ergodic Theory of Anosov Diffeomorphisms written by Robert Edward Bowen and published by Springer. This book was released on 2008-04-04 with total page 85 pages. Available in PDF, EPUB and Kindle. Book excerpt: For this printing of R. Bowen's book, J.-R. Chazottes has retyped it in TeX for easier reading, thereby correcting typos and bibliographic details. From the Preface by D. Ruelle: "Rufus Bowen has left us a masterpiece of mathematical exposition... Here a number of results which were new at the time are presented in such a clear and lucid style that Bowen's monograph immediately became a classic. More than thirty years later, many new results have been proved in this area, but the volume is as useful as ever because it remains the best introduction to the basics of the ergodic theory of hyperbolic systems."

Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields

Author : John Guckenheimer
Publisher : Springer Science & Business Media
ISBN 13 : 1461211409
Total Pages : 475 pages
Book Rating : 4.4/5 (612 download)

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Book Synopsis Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields by : John Guckenheimer

Download or read book Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields written by John Guckenheimer and published by Springer Science & Business Media. This book was released on 2013-11-21 with total page 475 pages. Available in PDF, EPUB and Kindle. Book excerpt: An application of the techniques of dynamical systems and bifurcation theories to the study of nonlinear oscillations. Taking their cue from Poincare, the authors stress the geometrical and topological properties of solutions of differential equations and iterated maps. Numerous exercises, some of which require nontrivial algebraic manipulations and computer work, convey the important analytical underpinnings of problems in dynamical systems and help readers develop an intuitive feel for the properties involved.

Lyapunov Exponents of Linear Cocycles

Author : Pedro Duarte
Publisher : Springer
ISBN 13 : 9462391246
Total Pages : 271 pages
Book Rating : 4.4/5 (623 download)

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Book Synopsis Lyapunov Exponents of Linear Cocycles by : Pedro Duarte

Download or read book Lyapunov Exponents of Linear Cocycles written by Pedro Duarte and published by Springer. This book was released on 2016-03-21 with total page 271 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of this monograph is to present a general method of proving continuity of Lyapunov exponents of linear cocycles. The method uses an inductive procedure based on a general, geometric version of the Avalanche Principle. The main assumption required by this method is the availability of appropriate large deviation type estimates for quantities related to the iterates of the base and fiber dynamics associated with the linear cocycle. We establish such estimates for various models of random and quasi-periodic cocycles. Our method has its origins in a paper of M. Goldstein and W. Schlag. Our present work expands upon their approach in both depth and breadth. We conclude this monograph with a list of related open problems, some of which may be treated using a similar approach.