Geometric And Ergodic Aspects Of Group Actions
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Author | : S. G. Dani |
Publisher | : Springer Nature |
Total Pages | : 176 |
Release | : 2020-01-13 |
Genre | : Mathematics |
ISBN | : 9811506833 |
This book gathers papers on recent advances in the ergodic theory of group actions on homogeneous spaces and on geometrically finite hyperbolic manifolds presented at the workshop “Geometric and Ergodic Aspects of Group Actions,” organized by the Tata Institute of Fundamental Research, Mumbai, India, in 2018. Written by eminent scientists, and providing clear, detailed accounts of various topics at the interface of ergodic theory, the theory of homogeneous dynamics, and the geometry of hyperbolic surfaces, the book is a valuable resource for researchers and advanced graduate students in mathematics.
Author | : Robert J. Zimmer |
Publisher | : University of Chicago Press |
Total Pages | : 724 |
Release | : 2019-12-23 |
Genre | : Mathematics |
ISBN | : 022656827X |
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.
Author | : Robert J. Zimmer |
Publisher | : University of Chicago Press |
Total Pages | : 659 |
Release | : 2011-04-15 |
Genre | : Mathematics |
ISBN | : 0226237893 |
The study of group actions is more than 100 years old but remains a widely studied topic in a variety of mathematic fields. A central development in the last 50 years is the phenomenon of rigidity, whereby one can classify actions of certain groups. This book looks at rigidity.
Author | : Sang-hyun Kim |
Publisher | : Springer |
Total Pages | : 140 |
Release | : 2019-01-02 |
Genre | : Mathematics |
ISBN | : 3030028550 |
In this partly expository work, a framework is developed for building exotic circle actions of certain classical groups. The authors give general combination theorems for indiscrete isometry groups of hyperbolic space which apply to Fuchsian and limit groups. An abundance of integer-valued subadditive defect-one quasimorphisms on these groups follow as a corollary. The main classes of groups considered are limit and Fuchsian groups. Limit groups are shown to admit large collections of faithful actions on the circle with disjoint rotation spectra. For Fuchsian groups, further flexibility results are proved and the existence of non-geometric actions of free and surface groups is established. An account is given of the extant notions of semi-conjugacy, showing they are equivalent. This book is suitable for experts interested in flexibility of representations, and for non-experts wanting an introduction to group representations into circle homeomorphism groups.
Author | : Mikhail Kapranov |
Publisher | : Springer Science & Business Media |
Total Pages | : 759 |
Release | : 2008-03-05 |
Genre | : Mathematics |
ISBN | : 3764386088 |
Alexander Reznikov (1960-2003) was a brilliant and highly original mathematician. This book presents 18 articles by prominent mathematicians and is dedicated to his memory. In addition it contains an influential, so far unpublished manuscript by Reznikov of book length. The book further provides an extensive survey on Kleinian groups in higher dimensions and some articles centering on Reznikov as a person.
Author | : S. Müller-Stach |
Publisher | : Cambridge University Press |
Total Pages | : 314 |
Release | : 2004-04-20 |
Genre | : Mathematics |
ISBN | : 9780521545471 |
Lecture notes for graduates or researchers wishing to enter this modern field of research.
Author | : Lizhen Ji |
Publisher | : |
Total Pages | : 602 |
Release | : 2015 |
Genre | : Group actions (Mathematics) |
ISBN | : 9781571463005 |
Author | : Cesar E. Silva |
Publisher | : Springer Nature |
Total Pages | : 707 |
Release | : 2023-07-31 |
Genre | : Mathematics |
ISBN | : 1071623885 |
This volume in the Encyclopedia of Complexity and Systems Science, Second Edition, covers recent developments in classical areas of ergodic theory, including the asymptotic properties of measurable dynamical systems, spectral theory, entropy, ergodic theorems, joinings, isomorphism theory, recurrence, nonsingular systems. It enlightens connections of ergodic theory with symbolic dynamics, topological dynamics, smooth dynamics, combinatorics, number theory, pressure and equilibrium states, fractal geometry, chaos. In addition, the new edition includes dynamical systems of probabilistic origin, ergodic aspects of Sarnak's conjecture, translation flows on translation surfaces, complexity and classification of measurable systems, operator approach to asymptotic properties, interplay with operator algebras
Author | : M. Bachir Bekka |
Publisher | : Cambridge University Press |
Total Pages | : 214 |
Release | : 2000-05-11 |
Genre | : Mathematics |
ISBN | : 9780521660303 |
This book, first published in 2000, focuses on developments in the study of geodesic flows on homogenous spaces.
Author | : Martin R. Bridson |
Publisher | : Cambridge University Press |
Total Pages | : 331 |
Release | : 2009-10-29 |
Genre | : Mathematics |
ISBN | : 052175724X |
An extended tour through a selection of the most important trends in modern geometric group theory.