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Saturday, April 18, 2020 | History

10 edition of Ergodic theory and semisimple groups found in the catalog.

Ergodic theory and semisimple groups

  • 117 Want to read
  • 27 Currently reading

Published by Birkhäuser in Boston .
Written in English

    Subjects:
  • Semisimple Lie groups.,
  • Ergodic theory.

  • Edition Notes

    StatementRobert J. Zimmer.
    SeriesMonographs in mathematics ;, v. 81
    Classifications
    LC ClassificationsQA387 .Z56 1984
    The Physical Object
    Paginationx, 209 p. ;
    Number of Pages209
    ID Numbers
    Open LibraryOL2848923M
    ISBN 100817631844
    LC Control Number84011127


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Ergodic theory and semisimple groups by Robert J. Zimmer Download PDF EPUB FB2

This book is based on a course given at the University of Chicago in 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.

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.

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 by: The more general modern theory treats the dynamical properties of the semisimple Lie groups.

Some of the most fundamental discoveries in this area are due to the work of G.A. Margulis and R. Zimmer. This book comprises a systematic, self-contained introduction to Ergodic theory and semisimple groups book Margulis-Zimmer theory, and provides an entry into current by: This book is based on a course given at the University of Chicago in 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.

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. COVID Resources. Reliable information about the coronavirus (COVID) is available from the World Health Organization (current situation, international travel).Numerous and frequently-updated resource results are available from this ’s WebJunction has pulled together information and resources to assist library staff as they consider how to handle coronavirus.

This book is based on a course given at the University of Chicago in 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.

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 Brand: R J Zimmer.

Ergodic Theory and Semisimple Groups. [Robert J Zimmer] -- This book is based on a course given at the University of Chicago in As with the course, the main motivation of this work is to present an accessible treatment, assuming minimal background.

The book Group Actions in Ergodic Theory, Geometry, and Topology: A. Strong Rigidity for Ergodic Actions of Semisimple Lie Groups, Annals of Mathematics () B. Orbit Equivalence and Rigidity of Ergodic Actions of Lie Groups, Ergodic Theory and Dynamical Systems ().

Ergodic theory and semisimple groups book LECTURES ON ERGODIC THEORY OF GROUP ACTIONS (A VON NEUMANN ALGEBRA APPROACH) SORIN POPA University of California, Los Angeles 1.

Group actions: basic properties Probability spaces as von Neumann algebras. The \classical" measure the-oretical approach to the study of actions of groups on the probability space is equivalent.

You can write a book review and share your experiences. Other readers will always be interested in your opinion of the books you've read. Whether you've loved the book or not, if you give your honest and detailed thoughts then people will find new books that are right for them.

() Example. The linear action of SL(n,R) on Rn factors through to a (nonlin- ear) action of SL(n,R) on the projective space RPn−1. More generally, SL(n,R) acts on Grassmannians, and other flag varieties.

Generalizing further, any semisimple Lie group Ghas transitive actions on some projective by: Ergodic Theory, Groups, and Geometry.

The study of group actions on manifolds is the meeting ground of a variety of mathematical areas. In particular, interesting geometric insights can be obtained by applying measure-theoretic techniques.3/5.

This book provides an introduction to dynamical systems and ergodic theory with an emphasis on smooth actions of noncompact Lie groups. The main goal is to serve as an entry into the literature on the ergodic theory of measure preserving actions of semisimple Lie groups/5(2).

Ergodic Theory and Semisimple Groups | This book is based on a course given at the University of Chicago in 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.

The study of group actions on manifolds is the meeting ground of a variety of mathematical areas. In particular, interesting geometric insights can be obtained by applying measure-theoretic techniques. This book provides an introduction to some of the important methods, major developments, and open problems in the subject.

The results established in this book constitute a new departure in ergodic theory and a significant expansion of its scope. Traditional ergodic theorems focused on amenable groups, and relied on the existence of an asymptotically invariant sequence in the group, the resulting maximal inequalities based on covering arguments, and the transference principle.

I think another good choice is the book "Ergodic Theory: With a View Towards Number Theory" by Manfred Einsiedler and Thomas Ward,Graduate Texts in Mathematics Besides basic concepts of ergodic theory,the book also discusses the connection between ergodic theory and number theory,which is a hot topic a forthcoming second volume will discuss about entropy,drafts of the book.

TY - JOUR AU - Zimmer, Robert J. TI - Ergodic theory, semisimple Lie groups and foliations by manifolds of negative curvature JO - Publications Mathématiques de l'IHÉS PY - PB - Institut des Hautes Études Scientifiques VL - 55 SP - 37 EP - 62 LA - eng KW - rigidity of ergodic actions of semisimple Lie groups; ergodic measurable foliations in which the leaves are Riemannian Cited by: In the book `Ergodic Theory and Semisimple groups' ( Edition, p Proposition ), Zimmer has made this statement "if G is a connected semisimple non-compact Lie group with finite center, then G admits an irreducible representation with a non-relatively compact projective image".

Cite this chapter as: Zimmer R.J. () Introduction. In: Ergodic Theory and Semisimple Groups. Monographs in Mathematics, vol Birkhäuser, Boston, MA. Available in: introduction to dynamical systems and ergodic theory with an emphasis on smooth actions of noncompact Lie groups.

Get FREE SHIPPING on Orders of $35+ Customer information on COVID B&N Outlet Membership Educators Gift Cards Stores & Events HelpPrice: $   Rational ergodicity, bounded rational ergodicity and some continuous measures on the circle, a collection of invited papers on ergodic theory.

Israel J. Math. 33 (3–4) ( Cited by: 7. Ergodic Theory and Semisimple Groups by R.J. Zimmer (English) Hardcover Book Fre Ergodic Theory and $ Theory Semisimple and Ergodic Groups New J R by Zimmer: Zimmer: by R Theory Groups New Semisimple J Ergodic and. Robert J.

Zimmer is president of the University of Chicago. He is the author of Ergodic Theory and Semisimple Groups and Essential Results of Functional Analysis and the co-author of Ergodic Theory, Groups, and Geometry.

He is also the author of more than eighty mathematical research articles. Ergodic Theory and Semisimple Groups.

点击放大图片 出版社: Birkhauser Boston. 作者: Zimmer; Zimmer, Robert J.; Zimmer, R. 出版时间: 年01月01 日. 10位国际标准书号: 13位国际. Book Description: The results established in this book constitute a new departure in ergodic theory and a significant expansion of its scope. Traditional ergodic theorems focused on amenable groups, and relied on the existence of an asymptotically invariant sequence in the group, the resulting maximal inequalities based on covering arguments, and the transference principle.

Hindustan Book Agency, Hyderabad, India,pp. – [33] Zimmer, R. Ergodic Theory and Semisimple Groups (Monographs in Mathematics, 81). Birkhäuser, Basel, Recommend this journal. Email your librarian or administrator to recommend adding this journal to your organisation's collection. The results established in this book constitute a new departure in ergodic theory and a significant expansion of its scope.

Traditional ergodic theorems focused on amenable groups, and relied on the existence of an asymptotically invariant sequence in the group, the resulting maximal inequalities based on covering arguments, and the transference ed on: Septem   This book is based on a course given at the University of Chicago in 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.

Margulis concerning rigidity, arithmeticity, and structure of lattices in semi simple groups, and related work of the author on the actions of semisimple groups Book Edition: Ed. Finally, we shall briefly discuss some applications of superrigidity in Riemannian geometry and also in characterization of lattices in higher rank simple Lie groups.

The main reference for the course will be the following book: Zimmer, Robert J. Ergodic theory and semisimple groups. Monographs in Mathematics, Birkhäuser Verlag, Basel, Gregori Aleksandrovich Margulis (Russian: григо́рий алекса́ндрович маргу́лис, first name often given as Gregory, Grigori or Grigory; born Febru ) is a Russian-American mathematician known for his work on lattices in Lie groups, and the introduction of methods from ergodic theory Awards: Fields Medal (), Lobachevsky Prize ().

The proofs of results on super-rigidity, arithmeticity and the noncentral normal subgroups of lattices in real semisimple Lie groups are also given in a monograph by R. Zimmer [Ergodic theory and semisimple groups, Birkhäuser, Basel, ; MR]. See e.g. Zimmer's book "Ergodic Theory and Semisimple Groups".

There the structure of the groups is crucial to the rigidity results. In particular, it's really ergodic theory that's used to prove Margulis' Normal Subgroup Theorem and Arithmeticity Theorem (both proved in Zimmer's book). In a different direction, the classical ergodic theory of Z-actions turns out to involve groups in a surprising way.

The Host-Kra. Discrete subgroups have played a central role throughout the development of numerous mathematical disciplines. Discontinuous group actions and the study of fundamental regions are of utmost importance to modern geometry.

Flows and dynamical systems on homogeneous spaces have found a wide range of applications, and of course number theory without discrete groups is unthinkable. The present book is devoted to lattices, i.e. discrete subgroups of finite covolume, in semi-simple Lie groups.

By "Lie groups" we not only mean real Lie groups, but also the sets of k-rational points of algebraic groups over local fields k and their direct products.

Our results can be applied to the theory of algebraic groups over global fields. Ergodic theory (Greek: έργον ergon "work", όδος hodos "way") is a branch of mathematics that studies dynamical systems with an invariant measure and related problems.

Its initial development was motivated by problems of statistical physics. Ergodic Theory, Groups, and Geometry. Robert J. Zimmer and Dave Witte Morris The notes provide an introduction to the study of the actions of a semisimple Lie group G on a manifold M.

This book is, I think, suitable for graduate students in the field; it is not an introduction to ergodic theory. Each lecture is a short survey on a topic. Locally symmetric spaces are generalizations of spaces of constant curvature. In this book the author presents the proof of a remarkable phenomenon, which he calls "strong rigidity": this is a stronger form of the deformation rigidity that has been investigated by Selberg, Calabi-Vesentini, Weil, Borel, and proof combines the theory of semi-simple Lie groups, discrete subgroups.

Destination page number Search scope Search Text. President Zimmer is the author of three books, Ergodic Theory and Semisimple Groups (), Essential Results of Functional Analysis (), and Ergodic Theory, Groups, and Geometry (); and more than 80 mathematical research articles.

I an amateur in ergodic theory myself, but I found the popular introductory text Ergodic Theory With a View Towards Number Theory to be an excellent text.

It's relevant for you since chapter 8 introduces actions of groups on dynamical systems, and the book specifies a minimal path for you to get to that point, chapters 2, 4 and 8 to be precise. Perhaps the most striking example of the ergodic theory of group actions is Margulis' proof that if G is a higher-rank semisimple Lie group (with trivial center) and [; \Gamma ;] is a lattice in G then every nontrivial normal subgroup of [; \Gamma ;] has finite index.There are several books dealing with lattices in semisimple Lie groups, the gentlest one, I think, is Introduction to Arithmetic Groups by Dave Witte Morris.

You can also read Zimmer's book Ergodic theory and semisimple groups or Raghunathan's book "Discrete subgroups of Lie groups" (both are still reasonably gentle); the hardest one to read.