Entropy, Lyapunov exponents, and rigidity of group actions
| Autor: | Michele Triestino, Bruno Santiago, Mario Roldán, Sébastien Alvarez, Dominique Malicet, Davi Obata, Aaron W. Brown |
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| Přispěvatelé: | University of Chicago, Laboratoire d'Analyse et de Mathématiques Appliquées (LAMA), Université Paris-Est Marne-la-Vallée (UPEM)-Fédération de Recherche Bézout-Université Paris-Est Créteil Val-de-Marne - Paris 12 (UPEC UP12)-Centre National de la Recherche Scientifique (CNRS), Universidade Federal Fluminense [Rio de Janeiro] (UFF), Institut de Mathématiques de Bourgogne [Dijon] (IMB), Université de Bourgogne (UB)-Centre National de la Recherche Scientifique (CNRS), Universidad de la República [Montevideo] (UCUR), Centre National de la Recherche Scientifique (CNRS)-Université Paris-Est Créteil Val-de-Marne - Paris 12 (UPEC UP12)-Fédération de Recherche Bézout-Université Paris-Est Marne-la-Vallée (UPEM), Centre National de la Recherche Scientifique (CNRS)-Université de Franche-Comté (UFC), Université Bourgogne Franche-Comté [COMUE] (UBFC)-Université Bourgogne Franche-Comté [COMUE] (UBFC)-Université de Bourgogne (UB), Université de Bourgogne (UB)-Université Bourgogne Franche-Comté [COMUE] (UBFC)-Centre National de la Recherche Scientifique (CNRS), Universidad de la República [Montevideo] (UDELAR), Triestino, Michele, université de Bourgogne, IMB |
| Jazyk: | angličtina |
| Rok vydání: | 2019 |
| Předmět: |
Pure mathematics
Primary 22F05 22E40. Secondary 37D25 37C85 [MATH.MATH-DS]Mathematics [math]/Dynamical Systems [math.DS] [MATH.MATH-DS] Mathematics [math]/Dynamical Systems [math.DS] Rigidity (psychology) Dynamical Systems (math.DS) Group Theory (math.GR) Mathematical proof 01 natural sciences Measure (mathematics) [MATH.MATH-GR]Mathematics [math]/Group Theory [math.GR] Group action 0103 physical sciences FOS: Mathematics Ergodic theory MSC : Primary: 22F05 22E40 Secondary: 37D25 37C85 0101 mathematics Abelian group Mathematics - Dynamical Systems Entropy (arrow of time) Mathematics [MATH.MATH-GR] Mathematics [math]/Group Theory [math.GR] 010102 general mathematics Lie group 010307 mathematical physics Mathematics - Group Theory |
| Zdroj: | Ensaios Matemáticos Ensaios Matemáticos, Brazilian Mathematical Society, 2019, Ensaios Matemáticos, 33, pp.1-197 {date} |
| ISSN: | 2175-0432 |
| Popis: | This text is an expanded series of lecture notes based on a 5-hour course given at the workshop entitled "Workshop for young researchers: Groups acting on manifolds" held in Teres\'opolis, Brazil in June 2016. The course introduced a number of classical tools in smooth ergodic theory -- particularly Lyapunov exponents and metric entropy -- as tools to study rigidity properties of group actions on manifolds. We do not present comprehensive treatment of group actions or general rigidity programs. Rather, we focus on two rigidity results in higher-rank dynamics: the measure rigidity theorem for affine Anosov abelian actions on tori due to A. Katok and R. Spatzier [Ergodic Theory Dynam. Systems 16, 1996] and recent the work of the main author with D. Fisher, S. Hurtado, F. Rodriguez Hertz, and Z. Wang on actions of lattices in higher-rank semisimple Lie groups on manifolds [arXiv:1608.04995; arXiv:1610.09997]. We give complete proofs of these results and present sufficient background in smooth ergodic theory needed for the proofs. A unifying theme in this text is the use of metric entropy and its relation to the geometry of conditional measures along foliations as a mechanism to verify invariance of measures. Comment: Final version (fixed typos). Main text by A. Brown, with 4 appendices by D. Malicet, D. Obata, B. Santiago and M. Triestino, S.Alvarez and M. Rold\'an. Edited by M. Triestino. To appear in Ensaios Matem\'aticos (by Brazilian Mathematical Society) |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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