Shadowing in Dynamical Systems
Published on 17. September 1999
Book
Paperback/Softback
XX, 276 pages
978-3-540-66299-0 (ISBN)
Description
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.
More details
Series
Edition
1999 ed.
Language
English
Place of publication
Berlin
Germany
Publishing group
Springer Berlin
Target group
Professional and scholarly
Research
Illustrations
XX, 276 p.
Dimensions
Height: 233 mm
Width: 155 mm
Thickness: 17 mm
Weight
448 gr
ISBN-13
978-3-540-66299-0 (9783540662990)
DOI
10.1007/BFb0093184
Schweitzer Classification
Content
Shadowing Near an Invariant Set
: Basic Definitions. Shadowing Near a Hyperbolic Set for a Diffeomorphism. Shadowing for Mappings of Banach Spaces. Limit Shadowing. Shadowing for Flows.-
Topologically Stable, Structurally
Stable, and Generic Systems
: Shadowing and Topological Stability. Shadowing in Structurally Stable Systems. Shadowing in Two-Dimensional Diffeomorphisms.
C
0-Genericity of Shadowing for Homeomorphisms.-
Systems with Special
Structure
: One-Dimensional Systems. Linear and Linearly Induced Systems. Lattice Systems. Global Attractors for Evolution Systems.-
Numerical Applications of Shadowing
: Finite Shadowing. Periodic Shadowing for Flows. Approximation of Spectral Characteristics. Approximation of the Morse Spectrum. Discretizations of PDEs.- References.- Index.