内容

目次

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