A Priori Bounds for H\'enon-like Renormalization
Dynamical Systems
2024-11-22 v1
Abstract
We formulate and prove 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.
Cite
@article{arxiv.2411.13624,
title = {A Priori Bounds for H\'enon-like Renormalization},
author = {Sylvain Crovisier and Mikhail Lyubich and Enrique Pujals and Jonguk Yang},
journal= {arXiv preprint arXiv:2411.13624},
year = {2024}
}
Comments
47 pages, 9 figures. arXiv admin note: substantial text overlap with arXiv:2411.08317