Download or read book Symbolic Dynamics and Hyperbolic Groups written by Michel Coornaert and published by Springer. This book was released on 2006-11-14 with total page 145 pages. Available in PDF, EPUB and Kindle. Book excerpt: Gromov's theory of hyperbolic groups have had a big impact in combinatorial group theory and has deep connections with many branches of mathematics suchdifferential geometry, representation theory, ergodic theory and dynamical systems. This book is an elaboration on some ideas of Gromov on hyperbolic spaces and hyperbolic groups in relation with symbolic dynamics. Particular attention is paid to the dynamical system defined by the action of a hyperbolic group on its boundary. The boundary is most oftenchaotic both as a topological space and as a dynamical system, and a description of this boundary and the action is given in terms of subshifts of finite type. The book is self-contained and includes two introductory chapters, one on Gromov's hyperbolic geometry and the other one on symbolic dynamics. It is intended for students and researchers in geometry and in dynamical systems, and can be used asthe basis for a graduate course on these subjects.
Download or read book Symbolic Dynamics and Hyperbolic Groups written by Michel Coornaert and published by . This book was released on 2014-01-15 with total page 148 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Ergodic Theory Symbolic Dynamics and Hyperbolic Spaces written by T. Bedford and published by Oxford University Press, USA. This book was released on 1991 with total page 369 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Horofunctions and Symbolic Dynamics on Gromov Hyperbolic Groups written by Michel Coornaert and published by . This book was released on 1998 with total page 51 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Ergodic Theory Symbolic Dynamics and Hyperbolic Spaces written by T. Bedford and published by Oxford University Press, USA. This book was released on 1991 with total page 369 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Symbolic Dynamics for Hyperbolic Surfaces of Finite Area written by Clara Bodelón and published by . This book was released on 2001 with total page 116 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Symbolic Dynamics written by Bruce P. Kitchens and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 263 pages. Available in PDF, EPUB and Kindle. Book excerpt: Nearly one hundred years ago Jacques Hadamard used infinite sequences of symbols to analyze the distribution of geodesics on certain surfaces. That was the beginning of symbolic dynamics. In the 1930's and 40's Arnold Hedlund and Marston Morse again used infinite sequences to investigate geodesics on surfaces of negative curvature. They coined the term symbolic dynamics and began to study sequence spaces with the shift transformation as dynamical systems. In the 1940's Claude Shannon used sequence spaces to describe infor mation channels. Since that time symbolic dynamics has been used in ergodic theory, topological dynamics, hyperbolic dynamics, information theory and complex dynamics. Symbolic dynamical systems with a finite memory are stud ied in this book. They are the topological Markov shifts. Each can be defined by transition rules and the rules can be summarized by a transition matrix. The study naturally divides into two parts. The first part is about topological Markov shifts where the alphabet is finite. The second part is concerned with topological Markov shifts whose alphabet is count ably infinite. The techniques used in the two cases are quite different. When the alphabet is finite most of the methods are combinatorial or algebraic. When the alphabet is infinite the methods are much more analytic. This book grew from notes for a graduate course taught at Wesleyan Uni versity in the fall of 1994 and is intended as a graduate text and as a reference book for mathematicians working in related fields.
Download or read book Groups and Topological Dynamics written by Volodymyr Nekrashevych and published by American Mathematical Society. This book was released on 2022-10-07 with total page 708 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is devoted to group-theoretic aspects of topological dynamics such as studying groups using their actions on topological spaces, using group theory to study symbolic dynamics, and other connections between group theory and dynamical systems. One of the main applications of this approach to group theory is the study of asymptotic properties of groups such as growth and amenability. The book presents recently developed techniques of studying groups of dynamical origin using the structure of their orbits and associated groupoids of germs, applications of the iterated monodromy groups to hyperbolic dynamical systems, topological full groups and their properties, amenable groups, groups of intermediate growth, and other topics. The book is suitable for graduate students and researchers interested in group theory, transformations defined by automata, topological and holomorphic dynamics, and theory of topological groupoids. Each chapter is supplemented by exercises of various levels of complexity.
Download or read book Essays in Group Theory written by S.M. Gersten and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 346 pages. Available in PDF, EPUB and Kindle. Book excerpt: Essays in Group Theory contains five papers on topics of current interest which were presented in a seminar at MSRI, Berkeley in June, 1985. Special mention should be given to Gromov`s paper, one of the most significant in the field in the last decade. It develops the theory of hyperbolic groups to include a version of small cancellation theory sufficiently powerful to recover deep results of Ol'shanskii and Rips. Each of the remaining papers, by Baumslag and Shalen, Gersten, Shalen, and Stallings contains gems. For example, the reader will delight in Stallings' explicit construction of free actions of orientable surface groups on R-trees. Gersten's paper lays the foundations for a theory of equations over groups and contains a very quick solution to conjugacy problem for a class of hyperbolic groups. Shalen's article reviews the rapidly expanding theory of group actions on R-trees and the Baumslag-Shalen article uses modular representation theory to establish properties of presentations whose relators are pth-powers.
Download or read book Symbolic Dynamics and Hyperbolic Dynamic Systems written by V. M. Alekseev and published by . This book was released on 1981 with total page 39 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Symbolic Dynamics written by Marston Morse and published by . This book was released on 1966 with total page 200 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Symbolic Dynamics and Hyperbolic Dynamic Systems written by Vladimir M. Alekseev and published by . This book was released on 1981 with total page 37 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Combinatorial and Geometric Group Theory written by Sean Cleary and published by American Mathematical Soc.. This book was released on 2002 with total page 290 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume grew out of two AMS conferences held at Columbia University (New York, NY) and the Stevens Institute of Technology (Hoboken, NJ) and presents articles on a wide variety of topics in group theory. Readers will find a variety of contributions, including a collection of over 170 open problems in combinatorial group theory, three excellent survey papers (on boundaries of hyperbolic groups, on fixed points of free group automorphisms, and on groups of automorphisms of compactRiemann surfaces), and several original research papers that represent the diversity of current trends in combinatorial and geometric group theory. The book is an excellent reference source for graduate students and research mathematicians interested in various aspects of group theory.
Download or read book Dynamical Systems Ergodic Theory and Probability in Memory of Kolya Chernov written by Alexander M. Blokh and published by American Mathematical Soc.. This book was released on 2017-09-18 with total page 330 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the Conference on Dynamical Systems, Ergodic Theory, and Probability, which was dedicated to the memory of Nikolai Chernov, held from May 18–20, 2015, at the University of Alabama at Birmingham, Birmingham, Alabama. The book is devoted to recent advances in the theory of chaotic and weakly chaotic dynamical systems and its applications to statistical mechanics. The papers present new original results as well as comprehensive surveys.
Download or read book Symbolic Dynamics and its Applications written by Susan G. Williams and published by American Mathematical Soc.. This book was released on 2004 with total page 168 pages. Available in PDF, EPUB and Kindle. Book excerpt: Symbolic dynamics originated as a tool for analyzing dynamical systems and flows by discretizing space as well as time. The development of information theory gave impetus to the study of symbol sequences as objects in their own right. Today, symbolic dynamics has expanded to encompass multi-dimensional arrays of symbols and has found diverse applications both within and beyond mathematics. This volume is based on the AMS Short Course on Symbolic Dynamics and its Applications. It contains introductory articles on the fundamental ideas of the field and on some of its applications. Topics include the use of symbolic dynamics techniques in coding theory and in complex dynamics, the relation between the theory of multi-dimensional systems and the dynamics of tilings, and strong shift equivalence theory. Contributors to the volume are experts in the field and are clear expositors. The book is suitable for graduate students and research mathematicians interested in symbolic dynamics and its applications.
Download or read book Dynamical Numbers Interplay between Dynamical Systems and Number Theory written by S. F. Koli︠a︡da and published by American Mathematical Soc.. This book was released on 2010 with total page 258 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains papers from the special program and international conference on Dynamical Numbers which were held at the Max-Planck Institute in Bonn, Germany in 2009. These papers reflect the extraordinary range and depth of the interactions between ergodic theory and dynamical systems and number theory. Topics covered in the book include stationary measures, systems of enumeration, geometrical methods, spectral methods, and algebraic dynamical systems.
Download or read book Equidistribution and Counting Under Equilibrium States in Negative Curvature and Trees written by Anne Broise-Alamichel and published by Springer Nature. This book was released on 2019-12-16 with total page 413 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a complete exposition of equidistribution and counting problems weighted by a potential function of common perpendicular geodesics in negatively curved manifolds and simplicial trees. Avoiding any compactness assumptions, the authors extend the theory of Patterson-Sullivan, Bowen-Margulis and Oh-Shah (skinning) measures to CAT(-1) spaces with potentials. The work presents a proof for the equidistribution of equidistant hypersurfaces to Gibbs measures, and the equidistribution of common perpendicular arcs between, for instance, closed geodesics. Using tools from ergodic theory (including coding by topological Markov shifts, and an appendix by Buzzi that relates weak Gibbs measures and equilibrium states for them), the authors further prove the variational principle and rate of mixing for the geodesic flow on metric and simplicial trees—again without the need for any compactness or torsionfree assumptions. In a series of applications, using the Bruhat-Tits trees over non-Archimedean local fields, the authors subsequently prove further important results: the Mertens formula and the equidistribution of Farey fractions in function fields, the equidistribution of quadratic irrationals over function fields in their completions, and asymptotic counting results of the representations by quadratic norm forms. One of the book's main benefits is that the authors provide explicit error terms throughout. Given its scope, it will be of interest to graduate students and researchers in a wide range of fields, for instance ergodic theory, dynamical systems, geometric group theory, discrete subgroups of locally compact groups, and the arithmetic of function fields.
