Shadowing in Dynamical Systems

Shadowing in Dynamical Systems

Author: Sergei Yu. Pilyugin

Publisher: Springer

ISBN: 9783540484295

Category: Mathematics

Page: 276

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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
Language: en
Pages: 276
Authors: Sergei Yu. Pilyugin
Categories: Mathematics
Type: BOOK - Published: 2006-11-14 - Publisher: Springer

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
Six Lectures on Dynamical Systems
Language: en
Pages: 312
Authors: Bernd Aulbach, Fritz Colonius
Categories: Mathematics
Type: BOOK - Published: 1996 - Publisher: World Scientific

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
Shadowing in Dynamical Systems
Language: en
Pages: 300
Authors: K.J. Palmer
Categories: Mathematics
Type: BOOK - Published: 2013-03-14 - Publisher: Springer Science & Business Media

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
Topology and Dynamics of Chaos
Language: en
Pages: 364
Authors: Christophe Letellier, Robert Gilmore
Categories: Mathematics
Type: BOOK - Published: 2013-01-11 - Publisher: World Scientific

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
Spaces of Dynamical Systems
Language: en
Pages: 244
Authors: Sergei Yu. Pilyugin
Categories: Science
Type: BOOK - Published: 2012-04-10 - Publisher: Walter de Gruyter

Dynamical systems are abundant in theoretical physics and engineering. Their understanding, with sufficient mathematical rigor, is vital to solving many problems. This work conveys the modern theory of dynamical systems in a didactically developed fashion. In addition to topological dynamics, structural stability and chaotic dynamics, also generic properties and pseudotrajectories