5 papers · 1 filter
MLC for parabolically bounded primitive renormalization
Jeremy Kahn, Alex Kapiamba, Mikhail Lyubich
We prove bounds and MLC (local connectivity of the Mandelbrot set ) for a class of infinitely renormalizable parameters whose renormalization type…
A priori bounds for some infinitely renormalizable quadratic: IV. Elephant Eyes
Jeremy Kahn, Misha Lyubich
In this paper we prove a priori bounds for an ``elephant eye'' combinatorics. Little -copies specifying these combinatorics are allowed to converge to the cusp of the Mandelbrot…
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…