Strong regularity
By: Pierre Berger & Jean-Christophe Yoccoz
Contributors: Yoccoz, Jean-Christophe, author
Series: Astérisque -- 410; Astérisque -- 410.
Publisher: Société Mathématique de France
Published: 2019
Place of publication: Paris
Language: eng
Number of pages: 177
ISBN-13: 9782856299043
Copyright date: 2019
Subjects: Attractors (Mathematics); Measure theory; Hyperbolic Differential equations; 31.41 real analysis
Description: "The strong regularity program was initiated by Jean-Christophe Yoccoz during his first lecture at Collège de France. As explained in the first article of this volume, this program aims to show the abundance of dynamics displaying a non-uniformly hyperbolic attractor. It proposes a topological and combinatorial definition of such mappings using the formalism of puzzle pieces. Their combinatorics enable to deduce the wished analytical properties. In 1997, this method enabled Jean-Christophe Yoccoz to give an alternative proof of the Jakobson theorem: the existence of a set of positive Lebesgue measure of parameters a such that the map x  x^2 + a has an attractor which is non-uniformly hyperbolic. This proof is the second article of this volume. In the third article, this method is generalized in dimension 2 by Pierre Berger to show the following theorem. For every C^2-perturbation of the family of maps (x, y)  (x^2 + a, 0), there exists a parameter set of positive Lebesgue measure at which these maps display a non-uniformly hyperbolic attractor. This gives in particular an alternative proof of the Benedicks-Carleson Theorem."--
Notes: Includes bibliographical references and index.

Translated from French.
Table of contents: title: Introduction  -- Pierre Berger & Jean-Christophe Yoccoz; title: A proof of Jakobson's theorem  -- Jean-Christophe Yoccoz; title: Abundance of non-uniformly hyperbolic Hénon-like endomorphisms -- Pierre Berger.