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arXiv · 2411.13624

A Priori Bounds for H\'enon-like Renormalization

Sylvain Crovisier·Mikhail Lyubich·Enrique Pujals·Jonguk Yang
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Abstract

We formulate and prove $\textit{a priori}$ bounds for the renormalization of H\'enon-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.

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Sylvain Crovisier, Mikhail Lyubich, Enrique Pujals, Jonguk Yang. 2024-11-20. A Priori Bounds for H\'enon-like Renormalization. https://arxiv.org/abs/2411.13624

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