4 papers
Critical set for surface diffeomorphisms revisited
Sylvain Crovisier, Enrique Pujals
We propose a notion of critical set for two-dimensional surface diffeomorphisms as an intrinsically defined object designed to play a role analogous to that of critical points in o…
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…
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…
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…