4 papers
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…