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math.DS2024
A Priori Bounds for Hénon-like Renormalization
Sylvain Crovisier, Mikhail Lyubich, Enrique Pujals +1
We formulate and prove bounds for the renormalization of Hénon-like maps (under certain regularity assumptions). This provides a certain uniform control on the…
math.DS2024
Quantitative Estimates on Invariant Manifolds for Surface Diffeomorphisms
Sylvain Crovisier, Mikhail Lyubich, Enrique Pujals +1
We carry out a detailed quantitative analysis on the geometry of invariant manifolds for smooth dissipative systems in dimension two. We begin by quantifying the regularity of any…
math.DS2024
Renormalization of Unicritical Diffeomorphisms of the Disk
Sylvain Crovisier, Mikhail Lyubich, Enrique Pujals +1
We introduce a class of infinitely renormalizable, unicritical diffeomorphisms of the disk (with a non-degenerate "critical point"). In this class of dynamical systems, we show tha…