Analysis of infinite dimensional dynamical systems by set-oriented numerics / von Adrian Ziessler ; [Gutachter: Prof. Dr. Michael Dellnitz, Prof. Dr. Oliver Junge]. Paderborn, 2018
Content
- 1 Introduction
- 2 Classical set-oriented techniques
- 2.1 Theoretical background
- 2.2 The subdivision algorithm
- 2.3 The continuation method
- 2.4 Computation of invariant measures
- 3 From finite to infinite dimensional embeddings
- 3.1 Taken's embedding theorem
- 3.2 Extension to fractal sets
- 3.3 Infinite dimensional embedding theory
- 4 The core dynamical system
- 5 Set-oriented techniques for embedded invariant sets
- 5.1 Extension to continuous dynamical systems
- 5.2 Computation of embedded attractors via subdivision
- 5.3 Continuation for embedded unstable manifolds
- 6 Applications
- 6.1 Delay differential equations
- 6.1.1 Numerical realization of the delay-coordinate map R
- 6.1.2 Numerical realization of the map E
- 6.1.3 Examples
- 6.2 Partial differential equations
- 7 Improving the numerical efficiency
- 7.1 A modified selection step for the subdivision algorithm
- 7.2 Development of a sequential procedure
- 7.3 Koopman operator based continuation step
- 8 Conclusion and outlook
- 8.1 The core dynamical system
- 8.2 Set-oriented techniques for embedded invariant sets
- 8.3 Improving the numerical efficiency
- 8.4 Future work
- Bibliography