Título:
Entropy, Lyapunov exponents, and rigidity of group actions
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Autor:
Brown, Aaron
Álvarez, Sebastien
Malicet, Dominique
Obata, Davi
Roldán, Mario
Santiago, Bruno
Triestino, Michele
Álvarez, Sebastien
Malicet, Dominique
Obata, Davi
Roldán, Mario
Santiago, Bruno
Triestino, Michele
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Tipo de documento:
Preprint
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Palabras clave:
Dynamical systems
Group Theory
Group Theory
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Año de publicación:
2019
Contenido:
Resumen:
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 Teresópolis, 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.
Descripción:
Publicado también como: Entropy, Lyapunov exponents, and rigidity of group actions / A. Brown, con apéndices de S. Alvarez , D. Malicet , D. Obata , B. Santiago , M. Triestino. Brasil : Sociedade Brasileira de Matemáticas. (Ensaios Matemáticos). ISBN: 978-85-8337-159-5
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Editorial:
arXiv
EN:
Mathematics (Dynamical Systems), arXiv:1809.09192, jun 2019, pp 1-160
Financiadores:
ANII: FCE_3_2018_1_148740
Citación:
Brown, A, Álvarez, S, Malicet, D, Obata, D, [y otros autores]. "Entropy, Lyapunov exponents, and rigidity of group actions" [Preprint]. Publicado en: Mathematics (Dynamical Systems). 2019 arXiv:1809.09192, jun 2019, pp 1-160.
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Licencia:
Licencia Creative Commons Atribución - No Comercial - Sin Derivadas (CC - By-NC-ND 4.0)
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| Ficheros | Descripción | Tamaño | Formato | ||
|---|---|---|---|---|---|
| 1809.09192.pdf | Preprint | 1.84 MB | Adobe PDF |