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Symbolic Dynamics And Hyperbolic Groups
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Book Synopsis Symbolic Dynamics and Hyperbolic Groups by : Michel Coornaert
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.
Book Synopsis Ergodic Theory, Symbolic Dynamics, and Hyperbolic Spaces by : T. Bedford
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:
Book Synopsis Symbolic Dynamics and Hyperbolic Groups by : Michel Coornaert
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:
Book Synopsis Symbolic Dynamics by : Bruce P. Kitchens
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.
Book Synopsis Essays in Group Theory by : S.M. Gersten
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.
Book Synopsis Combinatorial and Geometric Group Theory by : Sean Cleary
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.
Book Synopsis Dynamical Systems, Ergodic Theory, and Probability: in Memory of Kolya Chernov by : Alexander M. Blokh
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.
Book Synopsis Dynamical Numbers: Interplay between Dynamical Systems and Number Theory by : S. F. Koli︠a︡da
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.
Book Synopsis Equidistribution and Counting Under Equilibrium States in Negative Curvature and Trees by : Anne Broise-Alamichel
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 411 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.
Book Synopsis Groups St Andrews 1997 in Bath by : C. M. Campbell
Download or read book Groups St Andrews 1997 in Bath written by C. M. Campbell and published by Cambridge University Press. This book was released on 1999 with total page 396 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Groups, Geometry and Dynamics written by and published by . This book was released on 2007 with total page 652 pages. Available in PDF, EPUB and Kindle. Book excerpt: Publishes research articles that focus on groups or group actions as well as articles in other areas of mathematics in which groups or group actions are used as a main tool. Covers all topics of modern group theory with preference given to geometric, asymptotic and combinatorial group theory, dynamics of group actions, probabilistic and analytical methods, interaction with ergodic theory and operator algebras, and other related fields.
Book Synopsis Group Colorings and Bernoulli Subflows by : Su Gao
Download or read book Group Colorings and Bernoulli Subflows written by Su Gao and published by American Mathematical Soc.. This book was released on 2016-04-26 with total page 254 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper the authors study the dynamics of Bernoulli flows and their subflows over general countable groups. One of the main themes of this paper is to establish the correspondence between the topological and the symbolic perspectives. From the topological perspective, the authors are particularly interested in free subflows (subflows in which every point has trivial stabilizer), minimal subflows, disjointness of subflows, and the problem of classifying subflows up to topological conjugacy. Their main tool to study free subflows will be the notion of hyper aperiodic points; a point is hyper aperiodic if the closure of its orbit is a free subflow.
Book Synopsis Geometry of Lengths, Areas, and Volumes by : James W. Cannon
Download or read book Geometry of Lengths, Areas, and Volumes written by James W. Cannon and published by American Mathematical Soc.. This book was released on 2017-11-16 with total page 133 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the first of a three volume collection devoted to the geometry, topology, and curvature of 2-dimensional spaces. The collection provides a guided tour through a wide range of topics by one of the twentieth century's masters of geometric topology. The books are accessible to college and graduate students and provide perspective and insight to mathematicians at all levels who are interested in geometry and topology. The first volume begins with length measurement as dominated by the Pythagorean Theorem (three proofs) with application to number theory; areas measured by slicing and scaling, where Archimedes uses the physical weights and balances to calculate spherical volume and is led to the invention of calculus; areas by cut and paste, leading to the Bolyai-Gerwien theorem on squaring polygons; areas by counting, leading to the theory of continued fractions, the efficient rational approximation of real numbers, and Minkowski's theorem on convex bodies; straight-edge and compass constructions, giving complete proofs, including the transcendence of and , of the impossibility of squaring the circle, duplicating the cube, and trisecting the angle; and finally to a construction of the Hausdorff-Banach-Tarski paradox that shows some spherical sets are too complicated and cloudy to admit a well-defined notion of area.
Book Synopsis Topology as Fluid Geometry by : James W. Cannon
Download or read book Topology as Fluid Geometry written by James W. Cannon and published by American Mathematical Soc.. This book was released on 2017 with total page 181 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the second of a three volume collection devoted to the geometry, topology, and curvature of 2-dimensional spaces. The collection provides a guided tour through a wide range of topics by one of the twentieth century's masters of geometric topology. The books are accessible to college and graduate students and provide perspective and insight to mathematicians at all levels who are interested in geometry and topology. The second volume deals with the topology of 2-dimensional spaces. The attempts encountered in Volume 1 to understand length and area in the plane lead to examples most easily described by the methods of topology (fluid geometry): finite curves of infinite length, 1-dimensional curves of positive area, space-filling curves (Peano curves), 0-dimensional subsets of the plane through which no straight path can pass (Cantor sets), etc. Volume 2 describes such sets. All of the standard topological results about 2-dimensional spaces are then proved, such as the Fundamental Theorem of Algebra (two proofs), the No Retraction Theorem, the Brouwer Fixed Point Theorem, the Jordan Curve Theorem, the Open Mapping Theorem, the Riemann-Hurwitz Theorem, and the Classification Theorem for Compact 2-manifolds. Volume 2 also includes a number of theorems usually assumed without proof since their proofs are not readily available, for example, the Zippin Characterization Theorem for 2-dimensional spaces that are locally Euclidean, the Schoenflies Theorem characterizing the disk, the Triangulation Theorem for 2-manifolds, and the R. L. Moore's Decomposition Theorem so useful in understanding fractal sets.
Book Synopsis Encyclopedia of Nonlinear Science by : Alwyn Scott
Download or read book Encyclopedia of Nonlinear Science written by Alwyn Scott and published by Routledge. This book was released on 2006-05-17 with total page 2881 pages. Available in PDF, EPUB and Kindle. Book excerpt: In 438 alphabetically-arranged essays, this work provides a useful overview of the core mathematical background for nonlinear science, as well as its applications to key problems in ecology and biological systems, chemical reaction-diffusion problems, geophysics, economics, electrical and mechanical oscillations in engineering systems, lasers and nonlinear optics, fluid mechanics and turbulence, and condensed matter physics, among others.
Book Synopsis The Space of Dynamical Systems with the C0-Topology by : Sergei Yu. Pilyugin
Download or read book The Space of Dynamical Systems with the C0-Topology written by Sergei Yu. Pilyugin and published by Springer. This book was released on 2006-11-15 with total page 197 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is an introduction to main methods and principal results in the theory of Co(remark: o is upper index!!)-small perturbations of dynamical systems. It is the first comprehensive treatment of this topic. In particular, Co(upper index!)-generic properties of dynamical systems, topological stability, perturbations of attractors, limit sets of domains are discussed. The book contains some new results (Lipschitz shadowing of pseudotrajectories in structurally stable diffeomorphisms for instance). The aim of the author was to simplify and to "visualize" some basic proofs, so the main part of the book is accessible to graduate students in pure and applied mathematics. The book will also be a basic reference for researchers in various fields of dynamical systems and their applications, especially for those who study attractors or pseudotrajectories generated by numerical methods.
Book Synopsis Handbook of Teichmüller Theory by : Athanase Papadopoulos
Download or read book Handbook of Teichmüller Theory written by Athanase Papadopoulos and published by European Mathematical Society. This book was released on 2007 with total page 812 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Teichmuller space of a surface was introduced by O. Teichmuller in the 1930s. It is a basic tool in the study of Riemann's moduli spaces and the mapping class groups. These objects are fundamental in several fields of mathematics, including algebraic geometry, number theory, topology, geometry, and dynamics. The original setting of Teichmuller theory is complex analysis. The work of Thurston in the 1970s brought techniques of hyperbolic geometry to the study of Teichmuller space and its asymptotic geometry. Teichmuller spaces are also studied from the point of view of the representation theory of the fundamental group of the surface in a Lie group $G$, most notably $G=\mathrm{PSL}(2,\mathbb{R})$ and $G=\mathrm{PSL}(2,\mathbb{C})$. In the 1980s, there evolved an essentially combinatorial treatment of the Teichmuller and moduli spaces involving techniques and ideas from high-energy physics, namely from string theory. The current research interests include the quantization of Teichmuller space, the Weil-Petersson symplectic and Poisson geometry of this space as well as gauge-theoretic extensions of these structures. The quantization theories can lead to new invariants of hyperbolic 3-manifolds. The purpose of this handbook is to give a panorama of some of the most important aspects of Teichmuller theory. The handbook should be useful to specialists in the field, to graduate students, and more generally to mathematicians who want to learn about the subject. All the chapters are self-contained and have a pedagogical character. They are written by leading experts in the subject.
