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## Details

Genre/Form: | Electronic books |
---|---|

Additional Physical Format: | Print version: Navas, Andrés. Groups of Circle Diffeomorphisms. Chicago, IL : University of Chicago Press, ©2011 |

Material Type: | Document, Internet resource |

Document Type: | Internet Resource, Computer File |

All Authors / Contributors: |
Andrés Navas; Andreś Navas |

ISBN: | 9780226569505 0226569500 9780226569512 0226569519 1283362732 9781283362733 |

OCLC Number: | 772845711 |

Description: | 1 online resource (310 pages). |

Contents: | Introduction; Acknowledgments; Notation and General Definitions; 1. Examples of Group Actions on the Circle; 1.1 The Group of Rotations; 1.2 The Group of Translations and the Affine Group; 1.3 The Group PSL; 1.4 Actions of Lie Groups; 1.5 Thompson's Groups; 2. Dynamics of Groups of Homeomorphisms; 2.1 Minimal Invariant Sets; 2.2 Some Combinatorial Results; 2.3 Invariant Measures and Free Groups; 3. Dynamics of Groups of Diffeomorphisms; 3.1 Denjoy's Theorem; 3.2 Sacksteder's Theorem; 3.3 Duminy's First Theorem; 3.4 Duminy's Second Theorem; 3.5 Two Open Problems. 3.6 On the Smoothness of the Conjugacy between Groups of Diffeomorphisms4. Structure and Rigidity via Dynamical Methods; 4.1 Abelian Groups of Diffeomorphisms; 4.2 Nilpotent Groups of Diffeomorphisms; 4.3 Polycyclic Groups of Diffeomorphisms; 4.4 Solvable Groups of Diffeomorphisms; 4.5 On the Smooth Actions of Amenable Groups; 5. Rigidity via Cohomological Methods; 5.1 Thurston's Stability Theorem; 5.2 Rigidity for Groups with Kazhdan's Property (T); 5.3 Superrigidity for Higher-Rank Lattice Actions; Appendix A: Some Basic Concepts in Group Theory. Appendix B: Invariant Measures and Amenable GroupsReferences; Index. |

Series Title: | Chicago lectures in mathematics. |

### Abstract:

## Reviews

*Editorial reviews*

Publisher Synopsis

"Groups of Circle Diffeomorphisms provides a great overview of the research on differentiable group actions on the circle. Navas's book will appeal to those doing research on differential topology, transformation groups, dynamical systems, foliation theory, and representation theory, and will be a solid base for those who want to further attack problems of group actions on higher dimensional manifolds or of geometric group theory."--Takashi Tsuboi, University of Tokyo "This is a wonderful book about 'mildly' smooth actions of groups on the most important manifolds in mathematics: the circle and the line. Andres Navas draws upon the classical contributions of Poincare, Denjoy, Holder, Plante, Thompson, Sacksteder, and Duminy, as well as the relatively recent achievements of Margulis and Witte Morris, to offer the first book-length exploration of this topic. The analytic techniques, the dynamical point of view, and the algebraic nature of objects considered here produce a blend of beautiful mathematics that will be used by researchers in several areas of science."--Rostislav Grigorchuk, Texas A&M University, and Etienne Ghys, Ecole Normale Superieure de Lyon "Groups of Circle Diffeomorphisms provides a great overview of the research on differentiable group actions on the circle. Navas's book will appeal to those doing research on differential topology, transformation groups, dynamical systems, foliation theory, and representation theory, and will be a solid base for those who want to further attack problems of group actions on higher dimensional manifolds or of geometric group theory." --Takashi Tsuboi, University of Tokyo "This is a wonderful book about 'mildly' smooth actions of groups on the most important manifolds in mathematics: the circle and the line. Andres Navas draws upon the classical contributions of Poincare, Denjoy, Holder, Plante, Thompson, Sacksteder, and Duminy, as well as the relatively recent achievements of Margulis and Witte Morris, to offer the first book-length exploration of this topic. The analytic techniques, the dynamical point of view, and the algebraic nature of objects considered here produce a blend of beautiful mathematics that will be used by researchers in several areas of science." --Rostislav Grigorchuk, Texas A&M University, and Etienne Ghys, Ecole Normale Superieure de Lyon This is a wonderful book about mildly smooth actions of groups on the most important manifolds in mathematics: the circle and the line. Andres Navas draws upon the classical contributions of Poincare, Denjoy, Holder, Plante, Thompson, Sacksteder, and Duminy, as well as the relatively recent achievements of Margulis and Witte Morris, to offer the first book-length exploration of this topic. The analytic techniques, the dynamical point of view, and the algebraic nature of objects considered here produce a blend of beautiful mathematics that will be used by researchers in several areas of science. --Rostislav Grigorchuk, Texas A&M University, and Etienne Ghys, Ecole Normale Superieure de Lyon" "Groups of Circle Diffeomorphisms" provides a great overview of the research on differentiable group actions on the circle. Navas s book will appeal to those doing research on differential topology, transformation groups, dynamical systems, foliation theory, and representation theory, and will be a solid base for those who want to further attack problems of group actions on higher dimensional manifolds or of geometric group theory. --Takashi Tsuboi, University of Tokyo" ""Groups of Circle Diffeomorphisms" provides a great overview of the research on differentiable group actions on the circle. Navas's book will appeal to those doing research on differential topology, transformation groups, dynamical systems, foliation theory, and representation theory, and will be a solid base for those who want to further attack problems of group actions on higher dimensional manifolds or of geometric group theory."--Takashi Tsuboi, University of Tokyo Read more...

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