Dynamics Ergodic Theory And Geometry

Author : Boris Hasselblatt
Publisher : Cambridge University Press
Page : 324 pages
File Size : 46,5 Mb
Release : 2007-09-24
Category : Mathematics
ISBN : 9780521875417

Get Book

Dynamics, Ergodic Theory and Geometry by Boris Hasselblatt Pdf

Based on the subjects from the Clay Mathematics Institute/Mathematical Sciences Research Institute Workshop titled 'Recent Progress in Dynamics' in September and October 2004, this volume contains surveys and research articles by leading experts in several areas of dynamical systems that have experienced substantial progress. One of the major surveys is on symplectic geometry, which is closely related to classical mechanics and an exciting addition to modern geometry. The survey on local rigidity of group actions gives a broad and up-to-date account of another flourishing subject. Other papers cover hyperbolic, parabolic, and symbolic dynamics as well as ergodic theory. Students and researchers in dynamical systems, geometry, and related areas will find this book fascinating. The book also includes a fifty-page commented problem list that takes the reader beyond the areas covered by the surveys, to inspire and guide further research.

Author : Boris Hasselblatt
Publisher : Unknown
Page : 336 pages
File Size : 54,6 Mb
Release : 2007
Category : Differentiable dynamical systems
ISBN : 1139132903

Get Book

Dynamics, Ergodic Theory and Geometry by Boris Hasselblatt Pdf

Surveys, research articles, and commented problems in symplectic geometry, ergodicity, hyperbolic dynamics, and other areas.

Author : Hillel Furstenberg
Publisher : American Mathematical Society
Page : 82 pages
File Size : 41,6 Mb
Release : 2014-08-08
Category : Mathematics
ISBN : 9781470410346

Get Book

Ergodic Theory and Fractal Geometry by Hillel Furstenberg Pdf

Fractal geometry represents a radical departure from classical geometry, which focuses on smooth objects that "straighten out" under magnification. Fractals, which take their name from the shape of fractured objects, can be characterized as retaining their lack of smoothness under magnification. The properties of fractals come to light under repeated magnification, which we refer to informally as "zooming in". This zooming-in process has its parallels in dynamics, and the varying "scenery" corresponds to the evolution of dynamical variables. The present monograph focuses on applications of one branch of dynamics--ergodic theory--to the geometry of fractals. Much attention is given to the all-important notion of fractal dimension, which is shown to be intimately related to the study of ergodic averages. It has been long known that dynamical systems serve as a rich source of fractal examples. The primary goal in this monograph is to demonstrate how the minute structure of fractals is unfolded when seen in the light of related dynamics. A co-publication of the AMS and CBMS.

Author : Marc Burger,Alessandra Iozzi
Publisher : Springer Science & Business Media
Page : 494 pages
File Size : 44,7 Mb
Release : 2013-03-09
Category : Mathematics
ISBN : 9783662047439

Get Book

Rigidity in Dynamics and Geometry by Marc Burger,Alessandra Iozzi Pdf

This volume of proceedings is an offspring of the special semester Ergodic Theory, Geometric Rigidity and Number Theory which was held at the Isaac Newton Institute for Mathematical Sciences in Cambridge, UK, from Jan uary until July, 2000. Beside the activities during the semester, there were workshops held in January, March and July, the first being of introductory nature with five short courses delivered over a week. Although the quality of the workshops was excellent throughout the semester, the idea of these proceedings came about during the March workshop, which is hence more prominently represented, The format of the volume has undergone many changes, but what has remained untouched is the enthusiasm of the contributors since the onset of the project: suffice it to say that even though only two months elapsed between the time we contacted the potential authors and the deadline to submit the papers, the deadline was respected in the vast majority of the cases. The scope of the papers is not completely uniform throughout the volume, although there are some points in common. We asked the authors to write papers keeping in mind the idea that they should be accessible to students. At the same time, we wanted the papers not to be a summary of results that appeared somewhere else.

Author : Mariusz Urbański,Mario Roy,Sara Munday
Publisher : Walter de Gruyter GmbH & Co KG
Page : 458 pages
File Size : 55,6 Mb
Release : 2021-11-22
Category : Mathematics
ISBN : 9783110702682

Get Book

Ergodic Theory – Finite and Infinite, Thermodynamic Formalism, Symbolic Dynamics and Distance Expanding Maps by Mariusz Urbański,Mario Roy,Sara Munday Pdf

The book contains a detailed treatment of thermodynamic formalism on general compact metrizable spaces. Topological pressure, topological entropy, variational principle, and equilibrium states are presented in detail. Abstract ergodic theory is also given a significant attention. Ergodic theorems, ergodicity, and Kolmogorov-Sinai metric entropy are fully explored. Furthermore, the book gives the reader an opportunity to find rigorous presentation of thermodynamic formalism for distance expanding maps and, in particular, subshifts of finite type over a finite alphabet. It also provides a fairly complete treatment of subshifts of finite type over a countable alphabet. Transfer operators, Gibbs states and equilibrium states are, in this context, introduced and dealt with. Their relations are explored. All of this is applied to fractal geometry centered around various versions of Bowen’s formula in the context of expanding conformal repellors, limit sets of conformal iterated function systems and conformal graph directed Markov systems. A unique introduction to iteration of rational functions is given with emphasize on various phenomena caused by rationally indifferent periodic points. Also, a fairly full account of the classicaltheory of Shub’s expanding endomorphisms is given; it does not have a book presentation in English language mathematical literature.

Author : M. Bachir Bekka,Matthias Mayer
Publisher : Cambridge University Press
Page : 214 pages
File Size : 52,9 Mb
Release : 2000-05-11
Category : Mathematics
ISBN : 0521660300

Get Book

Ergodic Theory and Topological Dynamics of Group Actions on Homogeneous Spaces by M. Bachir Bekka,Matthias Mayer Pdf

This book, first published in 2000, focuses on developments in the study of geodesic flows on homogenous spaces.

Author : Robert J. Zimmer
Publisher : University of Chicago Press
Page : 724 pages
File Size : 50,6 Mb
Release : 2019-12-23
Category : Mathematics
ISBN : 9780226568270

Get Book

Group Actions in Ergodic Theory, Geometry, and Topology by Robert J. Zimmer Pdf

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 : Hillel Furstenberg
Publisher : Unknown
Page : 0 pages
File Size : 42,6 Mb
Release : 2017-06-05
Category : Mathematics
ISBN : 1470437260

Get Book

Ergodic Theory and Fractal Geometry by Hillel Furstenberg Pdf

fractal Geometry represents a radical departure from classical Geometry, which focuses on smooth objects that straighten out under magnification. Fractals, which take their name from the shape of fractured objects, can be characterized as retaining their lack of smoothness under magnification. The properties of fractals come to light under repeated magnification, which we refer to informally as zooming in. this zooming-in process has its parallels in dynamics, and the varying scenery corresponds to the evolution of dynamical variables. the present monograph focuses on applications of one branch of dynamics ergodic theory the Geometry of fractals. Much attention is given to the all-important notion of Fractal dimension, which is shown to be intimately related to the study of ergodic averages. It has been long known that dynamical systems serve as a rich source of Fractal examples. The primary goal in this monograph is to demonstrate how the minute structure of fractals is unfolded when seen in the light of related dynamics.

Author : Yves Coudène
Publisher : Springer
Page : 190 pages
File Size : 53,7 Mb
Release : 2016-11-10
Category : Mathematics
ISBN : 9781447172871

Get Book

Ergodic Theory and Dynamical Systems by Yves Coudène Pdf

This textbook is a self-contained and easy-to-read introduction to ergodic theory and the theory of dynamical systems, with a particular emphasis on chaotic dynamics. This book contains a broad selection of topics and explores the fundamental ideas of the subject. Starting with basic notions such as ergodicity, mixing, and isomorphisms of dynamical systems, the book then focuses on several chaotic transformations with hyperbolic dynamics, before moving on to topics such as entropy, information theory, ergodic decomposition and measurable partitions. Detailed explanations are accompanied by numerous examples, including interval maps, Bernoulli shifts, toral endomorphisms, geodesic flow on negatively curved manifolds, Morse-Smale systems, rational maps on the Riemann sphere and strange attractors. Ergodic Theory and Dynamical Systems will appeal to graduate students as well as researchers looking for an introduction to the subject. While gentle on the beginning student, the book also contains a number of comments for the more advanced reader.

Author : Sébastien Ferenczi,Joanna Kułaga-Przymus,Mariusz Lemańczyk
Publisher : Springer
Page : 434 pages
File Size : 51,7 Mb
Release : 2018-06-15
Category : Mathematics
ISBN : 9783319749082

Get Book

Ergodic Theory and Dynamical Systems in their Interactions with Arithmetics and Combinatorics by Sébastien Ferenczi,Joanna Kułaga-Przymus,Mariusz Lemańczyk Pdf

This book concentrates on the modern theory of dynamical systems and its interactions with number theory and combinatorics. The greater part begins with a course in analytic number theory and focuses on its links with ergodic theory, presenting an exhaustive account of recent research on Sarnak's conjecture on Möbius disjointness. Selected topics involving more traditional connections between number theory and dynamics are also presented, including equidistribution, homogenous dynamics, and Lagrange and Markov spectra. In addition, some dynamical and number theoretical aspects of aperiodic order, some algebraic systems, and a recent development concerning tame systems are described.

Author : Cesar E. Silva,Alexandre I. Danilenko
Publisher : Springer Nature
Page : 707 pages
File Size : 41,8 Mb
Release : 2023-07-31
Category : Mathematics
ISBN : 9781071623886

Get Book

Ergodic Theory by Cesar E. Silva,Alexandre I. Danilenko Pdf

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 : H. Broer,F. Takens,B. Hasselblatt
Publisher : Elsevier
Page : 560 pages
File Size : 46,7 Mb
Release : 2010-11-10
Category : Mathematics
ISBN : 0080932266

Get Book

Handbook of Dynamical Systems by H. Broer,F. Takens,B. Hasselblatt Pdf

In this volume, the authors present a collection of surveys on various aspects of the theory of bifurcations of differentiable dynamical systems and related topics. By selecting these subjects, they focus on those developments from which research will be active in the coming years. The surveys are intended to educate the reader on the recent literature on the following subjects: transversality and generic properties like the various forms of the so-called Kupka-Smale theorem, the Closing Lemma and generic local bifurcations of functions (so-called catastrophe theory) and generic local bifurcations in 1-parameter families of dynamical systems, and notions of structural stability and moduli. Covers recent literature on various topics related to the theory of bifurcations of differentiable dynamical systems Highlights developments that are the foundation for future research in this field Provides material in the form of surveys, which are important tools for introducing the bifurcations of differentiable dynamical systems

Author : Pei-Dong Liu,Min Qian
Publisher : Springer
Page : 233 pages
File Size : 48,7 Mb
Release : 2006-11-14
Category : Mathematics
ISBN : 9783540492917

Get Book

Smooth Ergodic Theory of Random Dynamical Systems by Pei-Dong Liu,Min Qian Pdf

This book studies ergodic-theoretic aspects of random dynam- ical systems, i.e. of deterministic systems with noise. It aims to present a systematic treatment of a series of recent results concerning invariant measures, entropy and Lyapunov exponents of such systems, and can be viewed as an update of Kifer's book. An entropy formula of Pesin's type occupies the central part. The introduction of relation numbers (ch.2) is original and most methods involved in the book are canonical in dynamical systems or measure theory. The book is intended for people interested in noise-perturbed dynam- ical systems, and can pave the way to further study of the subject. Reasonable knowledge of differential geometry, measure theory, ergodic theory, dynamical systems and preferably random processes is assumed.

Author : Anonim
Publisher : Academic Press
Page : 189 pages
File Size : 52,8 Mb
Release : 1976-11-15
Category : Mathematics
ISBN : 0080873863

Get Book

Ergodic Theory and Topological Dynamics by Anonim Pdf

Ergodic Theory and Topological Dynamics

Author : T. Bedford,Michael S. Keane,Caroline Series
Publisher : Oxford University Press, USA
Page : 369 pages
File Size : 52,5 Mb
Release : 1991
Category : Ergodic theory
ISBN : 019853390X

Get Book

Ergodic Theory, Symbolic Dynamics, and Hyperbolic Spaces by T. Bedford,Michael S. Keane,Caroline Series Pdf