Overview

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.

Full Product Details

Author:   Sergei Yu. Pilyugin
Publisher:   Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
Imprint:   Springer-Verlag Berlin and Heidelberg GmbH & Co. K
Edition:   1999 ed.
Volume:   1706
Dimensions:   Width: 15.50cm , Height: 1.50cm , Length: 23.50cm
Weight:   0.920kg
ISBN:  

9783540662990

ISBN 10:   3540662995
Pages:   276
Publication Date:   17 September 1999
Audience:   Professional and scholarly ,  Professional and scholarly ,  Professional & Vocational ,  Professional & Vocational
Format:   Paperback
Publisher's Status:   Active
Availability:   Out of print, replaced by POD  
We will order this item for you from a manufatured on demand supplier.

Table of Contents

Chapter 1. Shadowing Near an Invariant Set 1.1 Basic Definitions 1.2 Shadowing Near a Hyperbolic Set for a Diffeomorphism 1.2.1 Hyperbolic Sets 1.2.2 The Classical Shadowing Lemma 1.2.3 Shadowing for a Family of Approximate Trajectories 1.2.4 The Method of Bowen 1.3 Shadowing for Mappings of Banach Spaces 1.3.1 Shadowing for a Sequence of Mappings 1.3.2 Conditions of Uniqueness 1.3.3 Application to the Classical Shadowing Lemma 1.3.4 Theorems of Chow-Lin-Palmer and Steinlein-Walther 1.3.5 Finite-Dimensional Case 1.4 Limit Shadowing 1.4.1 Limit Shadowing Property 1.4.2 Lp-Shadowing 1.4.3 The Sacker-Sell Spectrum and Weighted Shadowing 1.4.4 Asymptotic Pseudotrajectories 1.5 Shadowing for Flows Chapter 2. Topologically Stable, Structurally Stable, and Generic Systems 2.1 Shadowing and Topological Stability 2.2 Shadowing in Structurally Stable Systems 2.2.1 The Case of a Flow 2.2.2 The Case of a Diffeomorphism 2.3 Shadowing in Two-Dimensional Diffeomorphisms 2.4 Co-Genericity of Shadowing for Homeomorphisms Chapter 3. Systems with Special Structure 3.1 One-Dimensional Systems 3.2 Linear and Linearly Induced Systems 3.3 Lattice Systems 3.4 Global Attractors for Evolution Systems Chapter 4. Numerical Applications of Shadowing 4.1 Finite Shadowing 4.2 Periodic Shadowing for Flows 4.3 Approximation of Spectral Characteristics 4.3.1 Evaluation of Upper Lyapunov Exponents 4.3.2 Approximation of the Morse Spectrum 4.4 Discretizations of PDEs 4.4.1 Shadowing in Discretizations 4.4.2 Discretization Errors on Unbounded Time Intervals

Reviews

Author Information

Tab Content 6

Author Website:  

Customer Reviews

Recent Reviews

No review item found!

Add your own review!

Countries Available

All regions