Softcover ISBN:  9782856299043 
Product Code:  AST/410 
List Price:  $75.00 
AMS Member Price:  $60.00 
Softcover ISBN:  9782856299043 
Product Code:  AST/410 
List Price:  $75.00 
AMS Member Price:  $60.00 

Book DetailsAstérisqueVolume: 410; 2019; 180 ppMSC: Primary 37
The strong regularity program was initiated by JeanChristophe 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 nonuniformly hyperbolic attractor. It proposes a topological and combinatorial definition of such mappings using the formalism of puzzle pieces. Their combinatorics make it possible to deduce the desired analytical properties.
In 1997, this method enabled JeanChritophe 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 \(x\mapsto x^2+a\) has an attractor which is nonuniformly 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 \((x,y)\mapsto (x^2+a, 0)\), there exists a parameter set of positive Lebesgue measure at which these maps display a nonuniformly hyperbolic attractor. This gives, in particular, an alternative proof of the BenedicksCarleson Theorem.
A publication of the Société Mathématique de France, Marseilles (SMF), distributed by the AMS in the U.S., Canada, and Mexico. Orders from other countries should be sent to the SMF. Members of the SMF receive a 30% discount from list.
ReadershipGraduate students and research mathematicians.

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The strong regularity program was initiated by JeanChristophe 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 nonuniformly hyperbolic attractor. It proposes a topological and combinatorial definition of such mappings using the formalism of puzzle pieces. Their combinatorics make it possible to deduce the desired analytical properties.
In 1997, this method enabled JeanChritophe 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 \(x\mapsto x^2+a\) has an attractor which is nonuniformly 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 \((x,y)\mapsto (x^2+a, 0)\), there exists a parameter set of positive Lebesgue measure at which these maps display a nonuniformly hyperbolic attractor. This gives, in particular, an alternative proof of the BenedicksCarleson Theorem.
A publication of the Société Mathématique de France, Marseilles (SMF), distributed by the AMS in the U.S., Canada, and Mexico. Orders from other countries should be sent to the SMF. Members of the SMF receive a 30% discount from list.
Graduate students and research mathematicians.