Strong regularity /

Strong regularity /

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Bibliographic Details
Author / Creator:	Berger, Pierre, 1980- author.
Imprint:	Paris : Société Mathématique de France [2019] ©2019
Description:	vii, 177 pages : illustrations ; 24 cm.
Language:	English
Series:	Astérisque, 0303-1179 ; 410 Astérisque ; 410.
Subject:	Measure theory. Differential equations, Hyperbolic. Attractors (Mathematics) Attractors (Mathematics) Differential equations, Hyperbolic. Measure theory.
Format:	Print Book
URL for this record:	http://pi.lib.uchicago.edu/1001/cat/bib/11925602

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Other authors / contributors:	Yoccoz, Jean-Christophe, author.
ISBN:	9782856299043 2856299040
Notes:	Includes bibliographical references and index. In English, with abstracts in English and French.
Summary:	"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."--

Description
Summary:	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^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.--
Physical Description:	vii, 177 pages : illustrations ; 24 cm.
Bibliography:	Includes bibliographical references and index.
ISBN:	9782856299043 2856299040
ISSN:	0303-1179 ;