Aubry–Mather Sets of the Breathing Circle Billiard
ABSTRACT Using variational techniques, we study the dynamics of the breathing circle billiard. We prove the existence of Aubry–Mather sets, which contain infinite subharmonic and generalized quasi‐periodic solutions, in arbitrarily high energy regions. This is under the assumption that the boundary motion is a periodic function. Additionally, our method provides a feasible approach to small twist problems and can be applied to some classical impact systems.
Authors
- Xianbin Liu (ORCID: https://orcid.org/0000-0002-6266-6153)
- Denghui Li (ORCID: https://orcid.org/0000-0001-5786-6313)
- Xiaoming Zhang (ORCID: https://orcid.org/0000-0002-1332-7665)
Institutions
- Jiangsu University of Technology (CN)
- Southwest Jiaotong University (CN)
- Nanjing University of Aeronautics and Astronautics (CN)
Publication Details
- Journal
- Mathematical Methods in the Applied Sciences
- Published
- 2025-05-19
- DOI
- https://doi.org/10.1002/mma.10996
- Primary Topic
- Mathematical Dynamics and Fractals
- Type
- article
- Field-Weighted Citation Impact
- 0.00
Funders
- National Natural Science Foundation of China