Work

A Priori Bounds for Hénon-like Renormalization

Year: 2024

Type: preprint

Abstract: 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.

Source: HAL (Le Centre pour la Communication Scientifique Directe)

DOI: 10.48550/arxiv.2411.13624

Authors: Crovisier, Sylvain, Lyubich, Mikhail, Pujals, Enrique, Yang, Jonguk

Institution: Laboratoire de Mathématiques d'Orsay

Language: English

Topic: Mathematical Dynamics and Fractals

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W4404649991

Cites:

Cited by:

Related to: 10