A Priori Bounds for Hénon-like Renormalization
Fuente:
arXiv
Salvato in:
| Autori principali: | , , , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2024
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866913582391754752 |
|---|---|
| author | Crovisier, Sylvain Lyubich, Mikhail Pujals, Enrique Yang, Jonguk |
| author_facet | Crovisier, Sylvain Lyubich, Mikhail Pujals, Enrique Yang, Jonguk |
| contents | We formulate and prove $\textit{a priori}$ bounds for the renormalization of Hénon-like maps (under certain regularity assumptions). This provides a certain uniform control on the small-scale geometry of the dynamics, and ensures pre-compactness of the renormalization sequence. In a sequel to this paper, a priori bounds are used in the proof of the main results, including renormalization convergence, finite-time checkability of the required regularity conditions and regular unicriticality of the dynamics. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_13624 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A Priori Bounds for Hénon-like Renormalization Crovisier, Sylvain Lyubich, Mikhail Pujals, Enrique Yang, Jonguk Dynamical Systems 37E20 (primary) 37E30, 37C05 (secondary) We formulate and prove $\textit{a priori}$ bounds for the renormalization of Hénon-like maps (under certain regularity assumptions). This provides a certain uniform control on the small-scale geometry of the dynamics, and ensures pre-compactness of the renormalization sequence. In a sequel to this paper, a priori bounds are used in the proof of the main results, including renormalization convergence, finite-time checkability of the required regularity conditions and regular unicriticality of the dynamics. |
| title | A Priori Bounds for Hénon-like Renormalization |
| topic | Dynamical Systems 37E20 (primary) 37E30, 37C05 (secondary) |
| url | https://arxiv.org/abs/2411.13624 |