| Softcover ISBN: | 978-2-85629-904-3 |
| Product Code: | AST/410 |
| List Price: | $75.00 |
| AMS Member Price: | $60.00 |
| Softcover ISBN: | 978-2-85629-904-3 |
| Product Code: | AST/410 |
| List Price: | $75.00 |
| AMS Member Price: | $60.00 |
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Book DetailsAstérisqueVolume: 410; 2019; 180 ppMSC: Primary 37
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 make it possible to deduce the desired analytical properties.
In 1997, this method enabled Jean-Chritophe 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 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 \((x,y)\mapsto (x^2+a, 0)\), 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.
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 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 make it possible to deduce the desired analytical properties.
In 1997, this method enabled Jean-Chritophe 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 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 \((x,y)\mapsto (x^2+a, 0)\), 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.
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.
