Strong regularity /
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| 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: | |
| Format: | Print Book |
| URL for this record: | http://pi.lib.uchicago.edu/1001/cat/bib/11925602 |
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| 050 | 4 | |a QA614.813 |b .B47 2019 | |
| 100 | 1 | |a Berger, Pierre, |d 1980- |e author. |0 http://id.loc.gov/authorities/names/no2019115239 |1 http://viaf.org/viaf/196164563 | |
| 245 | 1 | 0 | |a Strong regularity / |c Pierre Berger & Jean-Christophe Yoccoz. |
| 264 | 1 | |a Paris : |b Société Mathématique de France |c [2019] | |
| 264 | 4 | |c ©2019 | |
| 300 | |a vii, 177 pages : |b illustrations ; |c 24 cm. | ||
| 336 | |a text |b txt |2 rdacontent |0 http://id.loc.gov/vocabulary/contentTypes/txt | ||
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| 386 | |a French |2 lcdgt |0 http://id.loc.gov/authorities/demographicTerms/dg2015060737 | ||
| 386 | |a Men |2 lcdgt |0 http://id.loc.gov/authorities/demographicTerms/dg2015060359 | ||
| 490 | 1 | |a Astérisque, |x 0303-1179 ; |v 410 | |
| 504 | |a Includes bibliographical references and index. | ||
| 505 | 0 | 0 | |t Introduction / |r Pierre Berger & Jean-Christophe Yoccoz -- |t A proof of Jakobson's theorem / |r Jean-Christophe Yoccoz -- |t Abundance of non-uniformly hyperbolic Hénon-like endomorphisms / |r Pierre Berger. |
| 520 | 8 | |a "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."-- |c Back cover. | |
| 546 | |a In English, with abstracts in English and French. | ||
| 650 | 0 | |a Measure theory. |0 http://id.loc.gov/authorities/subjects/sh85082702 | |
| 650 | 0 | |a Differential equations, Hyperbolic. |0 http://id.loc.gov/authorities/subjects/sh85037899 | |
| 650 | 0 | |a Attractors (Mathematics) |0 http://id.loc.gov/authorities/subjects/sh97005887 | |
| 650 | 7 | |a Attractors (Mathematics) |2 fast |0 http://id.worldcat.org/fast/00820911 | |
| 650 | 7 | |a Differential equations, Hyperbolic. |2 fast |0 http://id.worldcat.org/fast/00893463 | |
| 650 | 7 | |a Measure theory. |2 fast |0 http://id.worldcat.org/fast/01013175 | |
| 650 | 7 | |a 31.41 real analysis. |0 (NL-LeOCL)077601963 |2 nbc | |
| 700 | 1 | |a Yoccoz, Jean-Christophe, |e author. |0 http://id.loc.gov/authorities/names/nr96011408 |1 http://viaf.org/viaf/49271428 | |
| 830 | 0 | |a Astérisque ; |v 410. |0 http://id.loc.gov/authorities/names/n86716119 | |
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| 927 | |t Library of Congress classification |a QA614.813.B47 2019 |l Eck |c Eck-Eck |g SEPS |b 116369366 |i 10146012 | ||