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Dimension Groups And Dynamical Systems
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Book Synopsis Dimension Groups and Dynamical Systems by : Fabien Durand
Download or read book Dimension Groups and Dynamical Systems written by Fabien Durand and published by Cambridge University Press. This book was released on 2022-02-03 with total page 594 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is the first self-contained exposition of the fascinating link between dynamical systems and dimension groups. The authors explore the rich interplay between topological properties of dynamical systems and the algebraic structures associated with them, with an emphasis on symbolic systems, particularly substitution systems. It is recommended for anybody with an interest in topological and symbolic dynamics, automata theory or combinatorics on words. Intended to serve as an introduction for graduate students and other newcomers to the field as well as a reference for established researchers, the book includes a thorough account of the background notions as well as detailed exposition – with full proofs – of the major results of the subject. A wealth of examples and exercises, with solutions, serve to build intuition, while the many open problems collected at the end provide jumping-off points for future research.
Book Synopsis Topological Dimension and Dynamical Systems by : Michel Coornaert
Download or read book Topological Dimension and Dynamical Systems written by Michel Coornaert and published by . This book was released on 2015 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Translated from the popular French edition, the goal of the book is to provide a self-contained introduction to mean topological dimension, an invariant of dynamical systems introduced in 1999 by Misha Gromov. The book examines how this invariant was successfully used by Elon Lindenstrauss and Benjamin Weiss to answer a long-standing open question about embeddings of minimal dynamical systems into shifts. A large number of revisions and additions have been made to the original text. Chapter 5 contains an entirely new section devoted to the Sorgenfrey line. Two chapters have also been added: Chapter 9 on amenable groups and Chapter 10 on mean topological dimension for continuous actions of countable amenable groups. These new chapters contain material that have never before appeared in textbook form. The chapter on amenable groups is based on Følner's characterization of amenability and may be read independently from the rest of the book. Although the contents of this book lead directly to several active areas of current research in mathematics and mathematical physics, the prerequisites needed for reading it remain modest; essentially some familiarities with undergraduate point-set topology and, in order to access the final two chapters, some acquaintance with basic notions in group theory. Topological Dimension and Dynamical Systems is intended for graduate students, as well as researchers interested in topology and dynamical systems. Some of the topics treated in the book directly lead to research areas that remain to be explored.
Book Synopsis Infinite-Dimensional Dynamical Systems in Mechanics and Physics by : Roger Temam
Download or read book Infinite-Dimensional Dynamical Systems in Mechanics and Physics written by Roger Temam and published by Springer Science & Business Media. This book was released on 2013-12-11 with total page 670 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this book the author presents the dynamical systems in infinite dimension, especially those generated by dissipative partial differential equations. This book attempts a systematic study of infinite dimensional dynamical systems generated by dissipative evolution partial differential equations arising in mechanics and physics and in other areas of sciences and technology. This second edition has been updated and extended.
Book Synopsis Dynamical Systems and Group Actions by : Lewis Bowen
Download or read book Dynamical Systems and Group Actions written by Lewis Bowen and published by American Mathematical Soc.. This book was released on 2012 with total page 264 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains cutting-edge research from leading experts in ergodic theory, dynamical systems and group actions. A large part of the volume addresses various aspects of ergodic theory of general group actions including local entropy theory, universal minimal spaces, minimal models and rank one transformations. Other papers deal with interval exchange transformations, hyperbolic dynamics, transfer operators, amenable actions and group actions on graphs.
Book Synopsis Dimension Theory in Dynamical Systems by : Yakov B. Pesin
Download or read book Dimension Theory in Dynamical Systems written by Yakov B. Pesin and published by University of Chicago Press. This book was released on 2008-04-15 with total page 633 pages. Available in PDF, EPUB and Kindle. Book excerpt: The principles of symmetry and self-similarity structure nature's most beautiful creations. For example, they are expressed in fractals, famous for their beautiful but complicated geometric structure, which is the subject of study in dimension theory. And in dynamics the presence of invariant fractals often results in unstable "turbulent-like" motions and is associated with "chaotic" behavior. In this book, Yakov Pesin introduces a new area of research that has recently appeared in the interface between dimension theory and the theory of dynamical systems. Focusing on invariant fractals and their influence on stochastic properties of systems, Pesin provides a comprehensive and systematic treatment of modern dimension theory in dynamical systems, summarizes the current state of research, and describes the most important accomplishments of this field. Pesin's synthesis of these subjects of broad current research interest will be appreciated both by advanced mathematicians and by a wide range of scientists who depend upon mathematical modeling of dynamical processes.
Book Synopsis Mathematics of Complexity and Dynamical Systems by : Robert A. Meyers
Download or read book Mathematics of Complexity and Dynamical Systems written by Robert A. Meyers and published by Springer Science & Business Media. This book was released on 2011-10-05 with total page 1885 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematics of Complexity and Dynamical Systems is an authoritative reference to the basic tools and concepts of complexity, systems theory, and dynamical systems from the perspective of pure and applied mathematics. Complex systems are systems that comprise many interacting parts with the ability to generate a new quality of collective behavior through self-organization, e.g. the spontaneous formation of temporal, spatial or functional structures. These systems are often characterized by extreme sensitivity to initial conditions as well as emergent behavior that are not readily predictable or even completely deterministic. The more than 100 entries in this wide-ranging, single source work provide a comprehensive explication of the theory and applications of mathematical complexity, covering ergodic theory, fractals and multifractals, dynamical systems, perturbation theory, solitons, systems and control theory, and related topics. Mathematics of Complexity and Dynamical Systems is an essential reference for all those interested in mathematical complexity, from undergraduate and graduate students up through professional researchers.
Book Synopsis Combinatorial Dynamics And Entropy In Dimension One by : Alseda Luis
Download or read book Combinatorial Dynamics And Entropy In Dimension One written by Alseda Luis and published by World Scientific Publishing Company. This book was released on 1993-06-04 with total page 344 pages. Available in PDF, EPUB and Kindle. Book excerpt: In last thirty years an explosion of interest in the study of nonlinear dynamical systems occured. The theory of one-dimensional dynamical systems has grown out in many directions. One of them has its roots in the Sharkovski0 Theorem. This beautiful theorem describes the possible sets of periods of all cycles of maps of an interval into itself. Another direction has its main objective in measuring the complexity of a system, or the amount of chaos present in it. A good way of doing this is to compute topological entropy of the system. The aim of this book is to provide graduate students and researchers with a unified and detailed exposition of these developments for interval and circle maps. Many comments are added referring to related problems, and historical remarks are made. Request Inspection Copy
Book Synopsis Structural Analysis of Complex Networks by : Matthias Dehmer
Download or read book Structural Analysis of Complex Networks written by Matthias Dehmer and published by Springer Science & Business Media. This book was released on 2010-10-14 with total page 493 pages. Available in PDF, EPUB and Kindle. Book excerpt: Filling a gap in literature, this self-contained book presents theoretical and application-oriented results that allow for a structural exploration of complex networks. The work focuses not only on classical graph-theoretic methods, but also demonstrates the usefulness of structural graph theory as a tool for solving interdisciplinary problems. Applications to biology, chemistry, linguistics, and data analysis are emphasized. The book is suitable for a broad, interdisciplinary readership of researchers, practitioners, and graduate students in discrete mathematics, statistics, computer science, machine learning, artificial intelligence, computational and systems biology, cognitive science, computational linguistics, and mathematical chemistry. It may also be used as a supplementary textbook in graduate-level seminars on structural graph analysis, complex networks, or network-based machine learning methods.
Book Synopsis Dynamics and Numbers by : Sergiǐ Kolyada:
Download or read book Dynamics and Numbers written by Sergiǐ Kolyada: and published by American Mathematical Soc.. This book was released on 2016-07-27 with total page 315 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains a collection of survey and research articles from the special program and international conference on Dynamics and Numbers held at the Max-Planck Institute for Mathematics in Bonn, Germany in 2014. The papers reflect the great diversity and depth of the interaction between number theory and dynamical systems and geometry in particular. Topics covered in this volume include symbolic dynamics, Bratelli diagrams, geometry of laminations, entropy, Nielsen theory, recurrence, topology of the moduli space of interval maps, and specification properties.
Book Synopsis Profinite Semigroups and Symbolic Dynamics by : Jorge Almeida
Download or read book Profinite Semigroups and Symbolic Dynamics written by Jorge Almeida and published by Springer Nature. This book was released on 2020-09-10 with total page 278 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book describes the relation between profinite semigroups and symbolic dynamics. Profinite semigroups are topological semigroups which are compact and residually finite. In particular, free profinite semigroups can be seen as the completion of free semigroups with respect to the profinite metric. In this metric, two words are close if one needs a morphism on a large finite monoid to distinguish them. The main focus is on a natural correspondence between minimal shift spaces (closed shift-invariant sets of two-sided infinite words) and maximal J-classes (certain subsets of free profinite semigroups). This correspondence sheds light on many aspects of both profinite semigroups and symbolic dynamics. For example, the return words to a given word in a shift space can be related to the generators of the group of the corresponding J-class. The book is aimed at researchers and graduate students in mathematics or theoretical computer science.
Book Synopsis Dimension Theory in Dynamical Systems by : Yakov B. Pesin
Download or read book Dimension Theory in Dynamical Systems written by Yakov B. Pesin and published by University of Chicago Press. This book was released on 1998-01-05 with total page 316 pages. Available in PDF, EPUB and Kindle. Book excerpt: The principles of symmetry and self-similarity structure nature's most beautiful creations. For example, they are expressed in fractals, famous for their beautiful but complicated geometric structure, which is the subject of study in dimension theory. And in dynamics the presence of invariant fractals often results in unstable "turbulent-like" motions and is associated with "chaotic" behavior. In this book, Yakov Pesin introduces a new area of research that has recently appeared in the interface between dimension theory and the theory of dynamical systems. Focusing on invariant fractals and their influence on stochastic properties of systems, Pesin provides a comprehensive and systematic treatment of modern dimension theory in dynamical systems, summarizes the current state of research, and describes the most important accomplishments of this field. Pesin's synthesis of these subjects of broad current research interest will be appreciated both by advanced mathematicians and by a wide range of scientists who depend upon mathematical modeling of dynamical processes.
Book Synopsis Combinatorics on Words by : Anna Frid
Download or read book Combinatorics on Words written by Anna Frid and published by Springer Nature. This book was released on 2023-05-30 with total page 310 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the 14th International Conference on Combinatorics on Words, WORDS 2023, held in Umeå, Sweden, during June 12–16, 2023. The 19 contributed papers presented in this book were carefully reviewed and selected from 28 submissions. In addition, the volume also contains 3 invited papers. WORDS is the main conference series devoted to combinatorics on words. This area is connected to several topics from computer science and mathematics, including string algorithms, automated proofs, discrete dynamics, number theory and, of course, classical combinatorics
Book Synopsis Cellular Automata and Complex Systems by : E. Goles
Download or read book Cellular Automata and Complex Systems written by E. Goles and published by Springer Science & Business Media. This book was released on 2013-11-27 with total page 187 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains the courses given at the Fifth School on Complex Systems held at Santiago, Chile, from 9th .to 13th December 1996. At this school met researchers working on areas related with recent trends in Complex Systems, which include dynamical systems, cellular automata, symbolic dynamics, spatial systems, statistical physics and thermodynamics. Scientists working in these subjects come from several areas: pure and applied mathematics, physics, biology, computer science and electrical engineering. Each contribution is devoted to one of the above subjects. In most cases they are structured as surveys, presenting at the same time an original point of view about the topic and showing mostly new results. The paper of Bruno Durand presents the state of the art on the relationships between the notions of surjectivity, injectivity and reversibility in cellular automata when finite, infinite or periodic configurations are considered, also he discusses decidability problems related with the classification of cellular automata as well as global properties mentioned above. The paper of Eric Goles and Martin Matamala gives a uniform presentation of simulations of Turing machines by cellular automata. The main ingredient is the encoding function which must be fixed for all Turing machine. In this context known results are revised and new results are presented.
Book Synopsis Advanced Topics in the Arithmetic of Elliptic Curves by : Joseph H. Silverman
Download or read book Advanced Topics in the Arithmetic of Elliptic Curves written by Joseph H. Silverman and published by Springer Science & Business Media. This book was released on 2013-12-01 with total page 528 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the introduction to the first volume of The Arithmetic of Elliptic Curves (Springer-Verlag, 1986), I observed that "the theory of elliptic curves is rich, varied, and amazingly vast," and as a consequence, "many important topics had to be omitted." I included a brief introduction to ten additional topics as an appendix to the first volume, with the tacit understanding that eventually there might be a second volume containing the details. You are now holding that second volume. it turned out that even those ten topics would not fit Unfortunately, into a single book, so I was forced to make some choices. The following material is covered in this book: I. Elliptic and modular functions for the full modular group. II. Elliptic curves with complex multiplication. III. Elliptic surfaces and specialization theorems. IV. Neron models, Kodaira-Neron classification of special fibers, Tate's algorithm, and Ogg's conductor-discriminant formula. V. Tate's theory of q-curves over p-adic fields. VI. Neron's theory of canonical local height functions.
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 Resolving Maps and the Dimension Group for Shifts of Finite Type by : Mike Boyle
Download or read book Resolving Maps and the Dimension Group for Shifts of Finite Type written by Mike Boyle and published by American Mathematical Soc.. This book was released on 1987 with total page 146 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Different Aspects of Coding Theory by : Robert Calderbank
Download or read book Different Aspects of Coding Theory written by Robert Calderbank and published by American Mathematical Soc.. This book was released on 1995 with total page 250 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
