Resolving Maps And The Dimension Group For Shifts Of Finite Type
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Resolving Maps And The Dimension Group For Shifts Of Finite Type
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Author : Mike Boyle
language : en
Publisher: American Mathematical Soc.
Release Date : 1987
Resolving Maps And The Dimension Group For Shifts Of Finite Type written by Mike Boyle and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1987 with Mathematics categories.
We give several results on necessary and sufficient conditions for the existence of special classes of maps from one shift of finite type onto another of the same entropy. The classes we study include eventual right closing maps, common right closing extensions, and stable right closing maps. Some analogous results for sofic systems are also given. The necessary and sufficient conditions are described algebraically in terms of the dimension group associated to a shift of finite type by W. Krieger.
Resolving Markov Chains Onto Bernoulli Shifts Via Positive Polynomials
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Author : Brian Marcus
language : en
Publisher: American Mathematical Soc.
Release Date : 2001
Resolving Markov Chains Onto Bernoulli Shifts Via Positive Polynomials written by Brian Marcus and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001 with Biography & Autobiography categories.
The two parts of this monograph contain two separate but related papers. The longer paper in Part A obtains necessary and sufficient conditions for several types of codings of Markov chains onto Bernoulli shifts. It proceeds by replacing the defining stochastic matrix of each Markov chain by a matrix whose entries are polynomials with positive coefficients in several variables; a Bernoulli shift is represented by a single polynomial with positive coefficients, $p$. This transforms jointly topological and measure-theoretic coding problems into combinatorial ones. In solving the combinatorial problems in Part A, the work states and makes use of facts from Part B concerning $p DEGREESn$ and its coefficients. Part B contains the shorter paper on $p DEGREESn$ and its coefficients, and is independ
Geometric And Probabilistic Structures In Dynamics
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Author : Keith Burns
language : en
Publisher: American Mathematical Soc.
Release Date : 2008
Geometric And Probabilistic Structures In Dynamics written by Keith Burns and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Mathematics categories.
"This book presents a collection of articles that cover areas of mathematics related to dynamical systems. The authors are well-known experts who use geometric and probabilistic methods to study interesting problems in the theory of dynamical systems and its applications. Some of the articles are surveys while others are original contributions. The topics covered include: Riemannian geometry, models in mathematical physics and mathematical biology, symbolic dynamics, random and stochastic dynamics. This book can be used by graduate students and researchers in dynamical systems and its applications."--BOOK JACKET.
Symbolic Dynamics And Its Applications
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Author : Susan G. Williams
language : en
Publisher: American Mathematical Soc.
Release Date : 2004
Symbolic Dynamics And Its Applications written by Susan G. Williams and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with Mathematics categories.
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.
Symbolic Dynamics
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Author : Bruce P. Kitchens
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Symbolic Dynamics written by Bruce P. Kitchens and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
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.
Combinatorial And Graph Theoretical Problems In Linear Algebra
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Author : Richard A. Brualdi
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Combinatorial And Graph Theoretical Problems In Linear Algebra written by Richard A. Brualdi and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
This IMA Volume in Mathematics and its Applications COMBINATORIAL AND GRAPH-THEORETICAL PROBLEMS IN LINEAR ALGEBRA is based on the proceedings of a workshop that was an integral part of the 1991-92 IMA program on "Applied Linear Algebra." We are grateful to Richard Brualdi, George Cybenko, Alan George, Gene Golub, Mitchell Luskin, and Paul Van Dooren for planning and implementing the year-long program. We especially thank Richard Brualdi, Shmuel Friedland, and Victor Klee for organizing this workshop and editing the proceedings. The financial support of the National Science Foundation made the workshop possible. A vner Friedman Willard Miller, Jr. PREFACE The 1991-1992 program of the Institute for Mathematics and its Applications (IMA) was Applied Linear Algebra. As part of this program, a workshop on Com binatorial and Graph-theoretical Problems in Linear Algebra was held on November 11-15, 1991. The purpose of the workshop was to bring together in an informal setting the diverse group of people who work on problems in linear algebra and matrix theory in which combinatorial or graph~theoretic analysis is a major com ponent. Many of the participants of the workshop enjoyed the hospitality of the IMA for the entire fall quarter, in which the emphasis was discrete matrix analysis.
Different Aspects Of Coding Theory
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Author : Robert Calderbank
language : en
Publisher: American Mathematical Soc.
Release Date : 1995
Different Aspects Of Coding Theory written by Robert Calderbank and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995 with Computers categories.
The symposia in applied mathematics have been held under the auspices of the American Mathematical Society and others since 1967. This books connects coding theory with actual applications in consumer electronics and with other areas of mathematics. It covers in detail the mathematical foundations of digital data storage and makes connections to symbolic dynamics, linear systems, and finite automata. It also explores the use of algebraic geometry within coding theory and examines links with finite geometry, statistics, and theoretical computer science.
Dynamical Systems
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Author : James C. Alexander
language : en
Publisher: Springer
Release Date : 2006-11-14
Dynamical Systems written by James C. Alexander and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-14 with Mathematics categories.
The papers in this volume reflect the richness and diversity of the subject of dynamics. Some are lectures given at the three conferences (Ergodic Theory and Topological Dynamics, Symbolic Dynamics and Coding Theory and Smooth Dynamics, Dynamics and Applied Dynamics) held in Maryland between October 1986 and March 1987; some are work which was in progress during the Special Year, and some are work which was done because of questions and problems raised at the conferences. In addition, a paper of John Milnor and William Thurston, versions of which had been available as notes but not yet published, is included.
Textile Systems For Endomorphisms And Automorphisms Of The Shift
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Author : Masakazu Nasu
language : en
Publisher: American Mathematical Soc.
Release Date : 1995
Textile Systems For Endomorphisms And Automorphisms Of The Shift written by Masakazu Nasu and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995 with Mathematics categories.
We introduce the notion of a textile system. Using this, we study the dynamical properties of endomorphisms and automorphisms of topological Markov shifts including one-sided ones. The dynamical properties of automorphisms of sofic systems are also studied.
An Introduction To Symbolic Dynamics And Coding
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Author : Douglas Lind
language : en
Publisher: Cambridge University Press
Release Date : 2021-01-21
An Introduction To Symbolic Dynamics And Coding written by Douglas Lind and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-01-21 with Language Arts & Disciplines categories.
Elementary introduction to symbolic dynamics, updated to describe the main advances in the subject since the original publication in 1995.