Invariant ruelle distributions for open hyperbolic systems : an analytical and numerical investigation / von Philipp Schütte ; betreut von Prof. Dr. Tobias Weich. Paderborn, 2024
Inhalt
- Analytical Study of Open Hyperbolic Systems
- Meromorphic Continuation of Weighted Zeta Functions
- The Geometric Setup
- Pollicott-Ruelle Resonances for Open Systems
- Expanded Proof of Meromorphic Continuation
- Remarks on Patterson-Sullivan Distributions
- Weighted Zetas for Convex Obstacle Scattering
- Weighted Zetas for Wigner Distributions
- Numerical Study of Convex-Cocompact Hyperbolic Surfaces
- Numerical Machinery
- Hyperbolic Map Systems and Dynamical Determinants
- Full Symmetry Reduction of Flow-Adapted Systems
- Dynamical Determinants beyond Hyperbolic Map Systems
- Numerical Investigation of Invariant Ruelle Distributions
- How to Visualize Invariant Ruelle Distributions
- Invariant Ruelle Distributions on the Fundamental Domain
- Resonance Sampling on Moduli Space
- Technical Implementation
- The PyZeta Project
- General Remarks on Technologies
- Programming Language and Development Environment
- Software Documentation and Version Control
- Testing Framework
- Measuring and Documenting Performance
- Optimizing Code
- Architecture and Internals of PyZeta
- Conclusion and Outlook
- The PyZEAL Project
- Appendices
- Meromorphic Continuation of Weighted Zeta Functions on Open Hyperbolic Systems
- Resonances and Weighted Zeta Functions for Obstacle Scattering via Smooth Models
- Invariant Ruelle Distributions on Convex-Cocompact Hyperbolic Surfaces
- Bibliography