Girod, Alina: (In)Finite Time Dynamical Systems with Homoclinic Structures – Discretization and Approximation –. 2019
Inhalt
- Introduction
- Basic Concepts
- Hyperbolicity
- Infinite Time Hyperbolicity
- Finite Time Hyperbolicity (M-Hyperbolicity)
- Finite and Infinite Time Hyperbolic Systems: Differences and Similarities
- Perturbation Results
- Stable and Unstable Subspaces and Cones
- Explicit Representations of (Un)Stable Subspaces and Cones
- -Norm and M-Hyperbolicity w.r.t. the -Norm
- D-Hyperbolicity
- An Explicit Representation of (Un)Stable Cones
- M-Hyperbolicity and D-Hyperbolicity
- Examples of 2-Dimensional D-Hyperbolic Systems
- Estimates for the Width of (Un)Stable Cones in 2-Dimensional Systems
- (Un)Stable Cones in 3- or Higher Dimensional D-Hyperbolic Systems
- Fiber Bundles in Finite and Infinite Time
- Monotonically (Un)Stable Ft-Fiber Bundles
- Monotonically -(Un)Stable Ft-Fiber Bundles
- -(Un)Stable Ft-Fiber Bundles
- Characteristics of the Ft-Fiber Bundles
- (Un)Stable Ft-Fiber Bundles and Ft-Hyperbolicity
- Local Approximation of (Ft-)Fiber Bundles
- An Algorithm to Calculate Fiber Bundles
- (In)Finite Time Homoclinic Trajectories
- Approximation of -Homoclinic Tubes and Numerical Tools
- Discretization by the h-Flow
- Discretization by a One-Step Method
- Applications
- An Artificial Example with Explicitly Known Homoclinic Orbits
- A Periodic Nonautonomous ODE
- An Example from Mathematical Biology
- A Lipschitz Inverse Mapping Theorem
- Assumptions, Functions, Sets
- Bibliography
- Index