Joint typical periodic optimization: systems with stable hyperbolicity
Fuente:
arXiv
Saved in:
| Main Authors: | , , , |
|---|---|
| Format: | Preprint |
| Published: |
2026
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866911691541839872 |
|---|---|
| author | Hao, Zelai Huang, Yinying Jenkinson, Oliver Li, Zhiqiang |
| author_facet | Hao, Zelai Huang, Yinying Jenkinson, Oliver Li, Zhiqiang |
| contents | The framework of joint typical periodic optimization, in which both the dynamical system and the potential function are allowed to vary simultaneously, was introduced in [HHJL25], in a direction motivated by the work of Yang, Hunt & Ott [YHO00]. For certain classes of hyperbolic systems, it was shown there that optimizing periodic orbits persist under simultaneous perturbation, yielding joint locking sets that contain open dense subsets of the relevant product spaces. In the present article we broaden the scope of this theory, by developing an axiomatic joint perturbation framework that accommodates a wider class of stably hyperbolic systems, and by establishing new joint typical periodic optimization results for several natural and important families: Axiom A diffeomorphisms with the no-cycle property, hyperbolic rational maps on the Riemann sphere, real quadratic polynomials, and $C^r$ maps in one dimension. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_01550 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Joint typical periodic optimization: systems with stable hyperbolicity Hao, Zelai Huang, Yinying Jenkinson, Oliver Li, Zhiqiang Dynamical Systems Primary: 37A99, Secondary: 37A05, 37D20, 37D35, 37E05, 37A44 The framework of joint typical periodic optimization, in which both the dynamical system and the potential function are allowed to vary simultaneously, was introduced in [HHJL25], in a direction motivated by the work of Yang, Hunt & Ott [YHO00]. For certain classes of hyperbolic systems, it was shown there that optimizing periodic orbits persist under simultaneous perturbation, yielding joint locking sets that contain open dense subsets of the relevant product spaces. In the present article we broaden the scope of this theory, by developing an axiomatic joint perturbation framework that accommodates a wider class of stably hyperbolic systems, and by establishing new joint typical periodic optimization results for several natural and important families: Axiom A diffeomorphisms with the no-cycle property, hyperbolic rational maps on the Riemann sphere, real quadratic polynomials, and $C^r$ maps in one dimension. |
| title | Joint typical periodic optimization: systems with stable hyperbolicity |
| topic | Dynamical Systems Primary: 37A99, Secondary: 37A05, 37D20, 37D35, 37E05, 37A44 |
| url | https://arxiv.org/abs/2605.01550 |