On the Dynamics of Invariant Graphs for Dissipative Twist Maps
Fuente:
arXiv
Salvato in:
| Autori principali: | , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2025
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866912480458964992 |
|---|---|
| author | Li, Qi Wang, Lin |
| author_facet | Li, Qi Wang, Lin |
| contents | For two-parameter families of dissipative twist maps, we investigate the dynamics of invariant graphs as well as the thresholds for their existence and breakdown. Our main results are as follows:
(1) For arbitrarily small $C^r$ perturbations with $r \geq 1$, invariant graphs with prescribed rotation numbers can be realized by adjusting the parameters;
(2) We characterize sharp perturbations that lead to the complete destruction of all invariant graphs;
(3) When the perturbation fails to be $C^1$, Lipschitz invariant graphs with non-differentiable points may still persist, even though the Lipschitz norm meets the conditions required by the normally hyperbolic invariant manifold theorem. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_04938 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the Dynamics of Invariant Graphs for Dissipative Twist Maps Li, Qi Wang, Lin Dynamical Systems Symplectic Geometry For two-parameter families of dissipative twist maps, we investigate the dynamics of invariant graphs as well as the thresholds for their existence and breakdown. Our main results are as follows: (1) For arbitrarily small $C^r$ perturbations with $r \geq 1$, invariant graphs with prescribed rotation numbers can be realized by adjusting the parameters; (2) We characterize sharp perturbations that lead to the complete destruction of all invariant graphs; (3) When the perturbation fails to be $C^1$, Lipschitz invariant graphs with non-differentiable points may still persist, even though the Lipschitz norm meets the conditions required by the normally hyperbolic invariant manifold theorem. |
| title | On the Dynamics of Invariant Graphs for Dissipative Twist Maps |
| topic | Dynamical Systems Symplectic Geometry |
| url | https://arxiv.org/abs/2506.04938 |