Symmetric homoclinic tangles in reversible dynamical systems have positive topological entropy
We consider reversible vector fields in R 2 n such that the set of fixed points of the involutory reversing symmetry is n -dimensional. Let such system have a smooth one-parameter family of symmetric periodic orbits which is of saddle type in normal directions. We establish that the topological entropy is positive when the stable and unstable manifolds of this family of periodic orbits have a strongly-transverse intersection.
Authors
- Ale Jan Homburg (ORCID: https://orcid.org/0000-0002-5411-2118)
- Jeroen S. W. Lamb (ORCID: https://orcid.org/0000-0001-7647-4200)
- Dmitry Turaev (ORCID: https://orcid.org/0000-0002-4637-6447)
Institutions
- Leiden University (NL)
- Gulf University for Science & Technology (KW)
- University of Applied Sciences Leiden (NL)
- Imperial College London (GB)
- Tokyo International University (JP)
- University of Amsterdam (NL)
Publication Details
- Journal
- Advances in Mathematics
- Published
- 2025-02-05
- DOI
- https://doi.org/10.1016/j.aim.2025.110131
- Primary Topic
- Quantum chaos and dynamical systems
- Type
- article
- Field-Weighted Citation Impact
- 0.00
Funders
- Leverhulme Trust
- Engineering and Physical Sciences Research Council
- Japan Science and Technology Agency