Download or read book Elements of Topological Dynamics written by J. de Vries and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 762 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is designed as an introduction into what I call 'abstract' Topological Dynamics (TO): the study of topological transformation groups with respect to problems that can be traced back to the qualitative theory of differential equa is in the tradition of the books [GH] and [EW. The title tions. So this book (,Elements . . . ' rather than 'Introduction . . . ') does not mean that this book should be compared, either in scope or in (intended) impact, with the 'Ele ments' of Euclid or Bourbaki. Instead, it reflects the choice and organisation of the material in this book: elementary and basic (but sufficient to understand recent research papers in this field). There are still many challenging prob lems waiting for a solution, and especially among general topologists there is a growing interest in this direction. However, the technical inaccessability of many research papers makes it almost impossible for an outsider to under stand what is going on. To a large extent, this inaccessability is caused by the lack of a good and systematic exposition of the fundamental methods and techniques of abstract TO. This book is an attempt to fill this gap. The guiding principle for the organization of the material in this book has been the exposition of methods and techniques rather than a discussion of the leading problems and their solutions. though the latter are certainly not neglected: they are used as a motivation wherever possible.
Download or read book Ergodic Theory and Topological Dynamics of Group Actions on Homogeneous Spaces written by M. Bachir Bekka and published by Cambridge University Press. This book was released on 2000-05-11 with total page 214 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book, first published in 2000, focuses on developments in the study of geodesic flows on homogenous spaces.
Download or read book Topological Dynamics written by Walter Helbig Gottschalk and published by American Mathematical Soc.. This book was released on 1955-01-01 with total page 184 pages. Available in PDF, EPUB and Kindle. Book excerpt: Topological dynamics is the study of transformation groups with respect to those topological properties whose prototype occurred in classical dynamics. In this volume, Part One contains the general theory. Part Two contains notable examples of flows which have contributed to the general theory of topological dynamics and which have in turn have been illuminated by the general theory of topological dynamics.
Download or read book Topological Dynamical Systems written by Jan Vries and published by Walter de Gruyter. This book was released on 2014-01-31 with total page 516 pages. Available in PDF, EPUB and Kindle. Book excerpt: There is no recent elementary introduction to the theory of discrete dynamical systems that stresses the topological background of the topic. This book fills this gap: it deals with this theory as 'applied general topology'. We treat all important concepts needed to understand recent literature. The book is addressed primarily to graduate students. The prerequisites for understanding this book are modest: a certain mathematical maturity and course in General Topology are sufficient.
Download or read book Groups and Topological Dynamics written by Volodymyr Nekrashevych and published by . This book was released on 2022 with total page 0 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.
Download or read book Official Illustrated Catalogue written by Weltausstellung (1862, London) and published by . This book was released on 1862 with total page 134 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Ordered Groups and Topology written by Adam Clay and published by American Mathematical Soc.. This book was released on 2016-11-16 with total page 154 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book deals with the connections between topology and ordered groups. It begins with a self-contained introduction to orderable groups and from there explores the interactions between orderability and objects in low-dimensional topology, such as knot theory, braid groups, and 3-manifolds, as well as groups of homeomorphisms and other topological structures. The book also addresses recent applications of orderability in the studies of codimension-one foliations and Heegaard-Floer homology. The use of topological methods in proving algebraic results is another feature of the book. The book was written to serve both as a textbook for graduate students, containing many exercises, and as a reference for researchers in topology, algebra, and dynamical systems. A basic background in group theory and topology is the only prerequisite for the reader.
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.
Download or read book Geometry and Dynamics of Groups and Spaces written by Mikhail Kapranov and published by Springer Science & Business Media. This book was released on 2008-03-05 with total page 742 pages. Available in PDF, EPUB and Kindle. Book excerpt: Alexander Reznikov (1960-2003) was a brilliant and highly original mathematician. This book presents 18 articles by prominent mathematicians and is dedicated to his memory. In addition it contains an influential, so far unpublished manuscript by Reznikov of book length. The book further provides an extensive survey on Kleinian groups in higher dimensions and some articles centering on Reznikov as a person.
Download or read book Invitation to C algebras and Topological Dynamics written by Jun Tomiyama and published by World Scientific. This book was released on 1987 with total page 180 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is an exposition on the interesting interplay between topological dynamics and the theory of C*-algebras. Researchers working in topological dynamics from various fields in mathematics are becoming more and more interested in this kind of algebraic approach of dynamics. This book is designed to present to the readers the subject in an elementary way, including also results of recent developments.
Download or read book Lectures on Topological Dynamics written by Robert Ellis and published by . This book was released on 1969 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Ergodic Theory written by Manfred Einsiedler and published by Springer Science & Business Media. This book was released on 2010-09-11 with total page 486 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text is a rigorous introduction to ergodic theory, developing the machinery of conditional measures and expectations, mixing, and recurrence. Beginning by developing the basics of ergodic theory and progressing to describe some recent applications to number theory, this book goes beyond the standard texts in this topic. Applications include Weyl's polynomial equidistribution theorem, the ergodic proof of Szemeredi's theorem, the connection between the continued fraction map and the modular surface, and a proof of the equidistribution of horocycle orbits. Ergodic Theory with a view towards Number Theory will appeal to mathematicians with some standard background in measure theory and functional analysis. No background in ergodic theory or Lie theory is assumed, and a number of exercises and hints to problems are included, making this the perfect companion for graduate students and researchers in ergodic theory, homogenous dynamics or number theory.
Download or read book Descriptive Set Theory and Dynamical Systems written by M. Foreman and published by Cambridge University Press. This book was released on 2000-05-25 with total page 304 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume, first published in 2000, contains a collection of survey papers providing an introduction for graduate students and researchers in these fields.
Download or read book Topology and Dynamics of Chaos written by Christophe Letellier and published by World Scientific. This book was released on 2013 with total page 362 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book surveys how chaotic behaviors can be described with topological tools and how this approach occurred in chaos theory. Some modern applications are included. The contents are mainly devoted to topology, the main field of Robert Gilmore's works in dynamical systems. They include a review on the topological analysis of chaotic dynamics, works done in the past as well as the very latest issues. Most of the contributors who published during the 90's, including the very well-known scientists Otto RAssler, Ren(r) Lozi and Joan Birman, have made a significant impact on chaos theory, discrete chaos, and knot theory, respectively. Very few books cover the topological approach for investigating nonlinear dynamical systems. The present book will provide not only some historical OCo not necessarily widely known OCo contributions (about the different types of chaos introduced by RAssler and not just the RAssler attractor; Gumowski and Mira's contributions in electronics; Poincar(r)'s heritage in nonlinear dynamics) but also some recent applications in laser dynamics, biology,
Download or read book Dynamics Topology and Numbers written by Pieter Moree and published by American Mathematical Soc.. This book was released on 2020-02-12 with total page 347 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the conference Dynamics: Topology and Numbers, held from July 2–6, 2018, at the Max Planck Institute for Mathematics, Bonn, Germany. The papers cover diverse fields of mathematics with a unifying theme of relation to dynamical systems. These include arithmetic geometry, flat geometry, complex dynamics, graph theory, relations to number theory, and topological dynamics. The volume is dedicated to the memory of Sergiy Kolyada and also contains some personal accounts of his life and mathematics.
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 Topological Theory of Dynamical Systems written by N. Aoki and published by Elsevier. This book was released on 1994-06-03 with total page 425 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph aims to provide an advanced account of some aspects of dynamical systems in the framework of general topology, and is intended for use by interested graduate students and working mathematicians. Although some of the topics discussed are relatively new, others are not: this book is not a collection of research papers, but a textbook to present recent developments of the theory that could be the foundations for future developments. This book contains a new theory developed by the authors to deal with problems occurring in diffentiable dynamics that are within the scope of general topology. To follow it, the book provides an adequate foundation for topological theory of dynamical systems, and contains tools which are sufficiently powerful throughout the book. Graduate students (and some undergraduates) with sufficient knowledge of basic general topology, basic topological dynamics, and basic algebraic topology will find little difficulty in reading this book.
