Ergodic Theory Semisimple Lie Groups And Foliations By Manifolds Of Negative Curvature
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Ergodic Theory Semisimple Lie Groups And Foliations By Manifolds Of Negative Curvature
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Author : Robert J. Zimmer
language : en
Publisher:
Release Date : 1982
Ergodic Theory Semisimple Lie Groups And Foliations By Manifolds Of Negative Curvature written by Robert J. Zimmer and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1982 with categories.
Ergodic Theory And Semisimple Groups
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Author : R.J. Zimmer
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-14
Ergodic Theory And Semisimple Groups written by R.J. Zimmer and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-14 with Mathematics categories.
This book is based on a course given at the University of Chicago in 1980-81. As with the course, the main motivation of this work is to present an accessible treatment, assuming minimal background, of the profound work of G. A. Margulis concerning rigidity, arithmeticity, and structure of lattices in semi simple groups, and related work of the author on the actions of semisimple groups and their lattice subgroups. In doing so, we develop the necessary prerequisites from earlier work of Borel, Furstenberg, Kazhdan, Moore, and others. One of the difficulties involved in an exposition of this material is the continuous interplay between ideas from the theory of algebraic groups on the one hand and ergodic theory on the other. This, of course, is not so much a mathematical difficulty as a cultural one, as the number of persons comfortable in both areas has not traditionally been large. We hope this work will also serve as a contribution towards improving that situation. While there are a number of satisfactory introductory expositions of the ergodic theory of integer or real line actions, there is no such exposition of the type of ergodic theoretic results with which we shall be dealing (concerning actions of more general groups), and hence we have assumed absolutely no knowledge of ergodic theory (not even the definition of "ergodic") on the part of the reader. All results are developed in full detail.
Ergodic Theory And Its Connection With Harmonic Analysis
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Author : Karl Endel Petersen
language : en
Publisher: Cambridge University Press
Release Date : 1995
Ergodic Theory And Its Connection With Harmonic Analysis written by Karl Endel Petersen and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995 with Ergodic theory categories.
Tutorial survey papers on important areas of ergodic theory, with related research papers.
Group Actions In Ergodic Theory Geometry And Topology
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Author : Robert J. Zimmer
language : en
Publisher: University of Chicago Press
Release Date : 2019-12-23
Group Actions In Ergodic Theory Geometry And Topology written by Robert J. Zimmer and has been published by University of Chicago Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-12-23 with Mathematics categories.
Robert J. Zimmer is best known in mathematics for the highly influential conjectures and program that bear his name. Group Actions in Ergodic Theory, Geometry, and Topology: Selected Papers brings together some of the most significant writings by Zimmer, which lay out his program and contextualize his work over the course of his career. Zimmer’s body of work is remarkable in that it involves methods from a variety of mathematical disciplines, such as Lie theory, differential geometry, ergodic theory and dynamical systems, arithmetic groups, and topology, and at the same time offers a unifying perspective. After arriving at the University of Chicago in 1977, Zimmer extended his earlier research on ergodic group actions to prove his cocycle superrigidity theorem which proved to be a pivotal point in articulating and developing his program. Zimmer’s ideas opened the door to many others, and they continue to be actively employed in many domains related to group actions in ergodic theory, geometry, and topology. In addition to the selected papers themselves, this volume opens with a foreword by David Fisher, Alexander Lubotzky, and Gregory Margulis, as well as a substantial introductory essay by Zimmer recounting the course of his career in mathematics. The volume closes with an afterword by Fisher on the most recent developments around the Zimmer program.
Foliations On Riemannian Manifolds
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Author : Philippe Tondeur
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Foliations On Riemannian Manifolds written by Philippe Tondeur and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
A first approximation to the idea of a foliation is a dynamical system, and the resulting decomposition of a domain by its trajectories. This is an idea that dates back to the beginning of the theory of differential equations, i.e. the seventeenth century. Towards the end of the nineteenth century, Poincare developed methods for the study of global, qualitative properties of solutions of dynamical systems in situations where explicit solution methods had failed: He discovered that the study of the geometry of the space of trajectories of a dynamical system reveals complex phenomena. He emphasized the qualitative nature of these phenomena, thereby giving strong impetus to topological methods. A second approximation is the idea of a foliation as a decomposition of a manifold into submanifolds, all being of the same dimension. Here the presence of singular submanifolds, corresponding to the singularities in the case of a dynamical system, is excluded. This is the case we treat in this text, but it is by no means a comprehensive analysis. On the contrary, many situations in mathematical physics most definitely require singular foliations for a proper modeling. The global study of foliations in the spirit of Poincare was begun only in the 1940's, by Ehresmann and Reeb.
Geometry Of Nonpositively Curved Manifolds
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Author : Patrick Eberlein
language : en
Publisher: University of Chicago Press
Release Date : 1996
Geometry Of Nonpositively Curved Manifolds written by Patrick Eberlein and has been published by University of Chicago Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996 with Mathematics categories.
Starting from the foundations, the author presents an almost entirely self-contained treatment of differentiable spaces of nonpositive curvature, focusing on the symmetric spaces in which every geodesic lies in a flat Euclidean space of dimension at least two. The book builds to a discussion of the Mostow Rigidity Theorem and its generalizations, and concludes by exploring the relationship in nonpositively curved spaces between geometric and algebraic properties of the fundamental group. This introduction to the geometry of symmetric spaces of non-compact type will serve as an excellent guide for graduate students new to the material, and will also be a useful reference text for mathematicians already familiar with the subject.
Geometry Of Foliations
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Author : Philippe Tondeur
language : en
Publisher: Birkhäuser
Release Date : 2012-12-06
Geometry Of Foliations written by Philippe Tondeur and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
The topics in this survey volume concern research done on the differential geom etry of foliations over the last few years. After a discussion of the basic concepts in the theory of foliations in the first four chapters, the subject is narrowed down to Riemannian foliations on closed manifolds beginning with Chapter 5. Following the discussion of the special case of flows in Chapter 6, Chapters 7 and 8 are de voted to Hodge theory for the transversal Laplacian and applications of the heat equation method to Riemannian foliations. Chapter 9 on Lie foliations is a prepa ration for the statement of Molino's Structure Theorem for Riemannian foliations in Chapter 10. Some aspects of the spectral theory for Riemannian foliations are discussed in Chapter 11. Connes' point of view of foliations as examples of non commutative spaces is briefly described in Chapter 12. Chapter 13 applies ideas of Riemannian foliation theory to an infinite-dimensional context. Aside from the list of references on Riemannian foliations (items on this list are referred to in the text by [ ]), we have included several appendices as follows. Appendix A is a list of books and surveys on particular aspects of foliations. Appendix B is a list of proceedings of conferences and symposia devoted partially or entirely to foliations. Appendix C is a bibliography on foliations, which attempts to be a reasonably complete list of papers and preprints on the subject of foliations up to 1995, and contains approximately 2500 titles.
Foliations Geometry And Topology
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Author : Nicolau Corção Saldanha
language : en
Publisher: American Mathematical Soc.
Release Date : 2009
Foliations Geometry And Topology written by Nicolau Corção Saldanha and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009 with Mathematics categories.
Presents the proceedings of the conference on Foliations, Geometry, and Topology, held August 6-10, 2007, in Rio de Janeiro, Brazil, in honor of the 70th birthday of Paul Schweitzer. The papers focus on the theory of foliations and related areas such as dynamical systems, group actions on low dimensional manifolds, and geometry of hypersurfaces.
Proceedings Of The Euroworkshop On Foliations Geometry And Dynamics 29 May 9 June 2000 Warsaw Poland
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Author : Pawe? Grzegorz Walczak
language : en
Publisher: World Scientific
Release Date : 2002
Proceedings Of The Euroworkshop On Foliations Geometry And Dynamics 29 May 9 June 2000 Warsaw Poland written by Pawe? Grzegorz Walczak and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002 with Mathematics categories.
Contains surveys and research articles regarding different aspects of the theory of foliation.
Foliations Geometry And Dynamics Proceedings Of The Euroworkshop
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Author : Lawrence Conlon
language : en
Publisher: World Scientific
Release Date : 2002-02-01
Foliations Geometry And Dynamics Proceedings Of The Euroworkshop written by Lawrence Conlon and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002-02-01 with categories.
This volume contains surveys and research articles regarding different aspects of the theory of foliation. The main aspects concern the topology of foliations of low-dimensional manifolds, the geometry of foliated Riemannian manifolds and the dynamical properties of foliations. Among the surveys are lecture notes devoted to the analysis of some operator algebras on foliated manifolds and the theory of confoliations (objects defined recently by W Thurston and Y Eliashberg, situated between foliations and contact structures). Among the research articles one can find a detailed proof of an unpublished theorem (due to Duminy) concerning ends of leaves in exceptional minimal sets.