Algebraic And Topological Dynamics

Author : S. F. Koli͡ada,Thomas Ward
Publisher : American Mathematical Soc.
Page : 364 pages
File Size : 46,8 Mb
Release : 2005
Category : Mathematics
ISBN : 9780821837511

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Algebraic and Topological Dynamics by S. F. Koli͡ada,Thomas Ward Pdf

This volume contains a collection of articles from the special program on algebraic and topological dynamics and a workshop on dynamical systems held at the Max-Planck Institute (Bonn, Germany). It reflects the extraordinary vitality of dynamical systems in its interaction with a broad range of mathematical subjects. Topics covered in the book include asymptotic geometric analysis, transformation groups, arithmetic dynamics, complex dynamics, symbolic dynamics, statistical properties of dynamical systems, and the theory of entropy and chaos. The book is suitable for graduate students and researchers interested in dynamical systems.

Author : N. Aoki,K. Hiraide
Publisher : Elsevier
Page : 425 pages
File Size : 54,6 Mb
Release : 1994-06-03
Category : Mathematics
ISBN : 9780080887210

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Topological Theory of Dynamical Systems by N. Aoki,K. Hiraide Pdf

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.

Author : Jun Tomiyama
Publisher : World Scientific
Page : 179 pages
File Size : 48,8 Mb
Release : 1987-10-01
Category : Mathematics
ISBN : 9789814507790

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Invitation To C*-algebras And Topological Dynamics by Jun Tomiyama Pdf

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.

Author : David B. Ellis,Robert Ellis
Publisher : Cambridge University Press
Page : 283 pages
File Size : 44,6 Mb
Release : 2014-06-05
Category : Mathematics
ISBN : 9781107633223

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Automorphisms and Equivalence Relations in Topological Dynamics by David B. Ellis,Robert Ellis Pdf

A lucid and self-contained treatment of many key ideas in topological dynamics, achieved by focusing on equivalence relations and automorphisms.

Author : Robert L. Devaney,Kit C. Chan,P.B. Vinod Kumar
Publisher : Springer Nature
Page : 278 pages
File Size : 52,7 Mb
Release : 2021-09-23
Category : Mathematics
ISBN : 9789811601743

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Topological Dynamics and Topological Data Analysis by Robert L. Devaney,Kit C. Chan,P.B. Vinod Kumar Pdf

This book collects select papers presented at the International Workshop and Conference on Topology & Applications, held in Kochi, India, from 9–11 December 2018. The book discusses topics on topological dynamical systems and topological data analysis. Topics are ranging from general topology, algebraic topology, differential topology, fuzzy topology, topological dynamical systems, topological groups, linear dynamics, dynamics of operator network topology, iterated function systems and applications of topology. All contributing authors are eminent academicians, scientists, researchers and scholars in their respective fields, hailing from around the world. The book is a valuable resource for researchers, scientists and engineers from both academia and industry.

Author : Pieter Moree,Anke Pohl,L’ubomír Snoha,Tom Ward
Publisher : American Mathematical Soc.
Page : 347 pages
File Size : 44,9 Mb
Release : 2020-02-12
Category : Education
ISBN : 9781470451004

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Dynamics: Topology and Numbers by Pieter Moree,Anke Pohl,L’ubomír Snoha,Tom Ward Pdf

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.

Author : Mike Field
Publisher : World Scientific
Page : 493 pages
File Size : 46,6 Mb
Release : 2007
Category : Mathematics
ISBN : 9781860948282

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Dynamics and Symmetry by Mike Field Pdf

This book contains the first systematic exposition of the global and local theory of dynamics equivariant with respect to a (compact) Lie group. Aside from general genericity and normal form theorems on equivariant bifurcation, it describes many general families of examples of equivariant bifurcation and includes a number of novel geometric techniques, in particular, equivariant transversality. This important book forms a theoretical basis of future work on equivariant reversible and Hamiltonian systems.This book also provides a general and comprehensive introduction to codimension one equivariant bifurcation theory. In particular, it includes the bifurcation theory developed with Roger Richardson on subgroups of reflection groups and the Maximal Isotropy Subgroup Conjecture. A number of general results are also given on the global theory. Introductory material on groups, representations and G-manifolds are covered in the first three chapters of the book. In addition, a self-contained introduction of equivariant transversality is given, including necessary results on stratifications as well as results on equivariant jet transversality developed by Edward Bierstone.

Author : Klaus Schmidt
Publisher : Springer Science & Business Media
Page : 323 pages
File Size : 46,8 Mb
Release : 2012-01-05
Category : Mathematics
ISBN : 9783034802765

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Dynamical Systems of Algebraic Origin by Klaus Schmidt Pdf

Although much of classical ergodic theory is concerned with single transformations and one-parameter flows, the subject inherits from statistical mechanics not only its name, but also an obligation to analyze spatially extended systems with multidimensional symmetry groups. However, the wealth of concrete and natural examples which has contributed so much to the appeal and development of classical dynamics, is noticeably absent in this more general theory. The purpose of this book is to help remedy this scarcity of explicit examples by introducing​ a class of continuous Zd-actions diverse enough to exhibit many of the new phenomena encountered in the transition from Z to Zd, but which nevertheless lends itself to systematic study: the Zd-actions by automorphisms of compact, abelian groups. One aspect of these actions, not surprising in itself but quite striking in its extent and depth nonetheless, is the connection with commutative algebra and arithmetical algebraic geometry. The algebraic framework resulting from this connection allows the construction of examples with a variety of specified dynamical properties, and by combining algebraic and dynamical tools one obtains a quite detailed understanding of this class of Zd-actions.

Author : Roy L. Adler,Peter Walters
Publisher : American Mathematical Soc.
Page : 451 pages
File Size : 53,6 Mb
Release : 1992
Category : Mathematics
ISBN : 9780821851463

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Symbolic Dynamics and Its Applications by Roy L. Adler,Peter Walters Pdf

This volume contains the proceedings of the conference, Symbolic Dynamics and its Applications, held at Yale University in the summer of 1991 in honor of Roy L. Adler on his sixtieth birthday. The conference focused on symbolic dynamics and its applications to other fields, including ergodic theory, smooth dynamical systems, information theory, automata theory, and statistical mechanics. One hundred thirty-nine participants attended from thirteen countries, representing mathematics, applied mathematics, electrical engineering, and physics departments in universities and in industry. Featuring a range of contributions from some of the leaders in the field, this volume presents an excellent overview of the subject.

Author : Volodymyr Nekrashevych
Publisher : American Mathematical Society
Page : 708 pages
File Size : 41,8 Mb
Release : 2022-10-11
Category : Mathematics
ISBN : 9781470471200

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Groups and Topological Dynamics by Volodymyr Nekrashevych Pdf

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.

Author : Anima Nagar,Manpreet Singh
Publisher : Springer Nature
Page : 87 pages
File Size : 42,5 Mb
Release : 2023-01-01
Category : Mathematics
ISBN : 9789811978777

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Topological Dynamics of Enveloping Semigroups by Anima Nagar,Manpreet Singh Pdf

This book introduces the theory of enveloping semigroups—an important tool in the field of topological dynamics—introduced by Robert Ellis. The book deals with the basic theory of topological dynamics and touches on the advanced concepts of the dynamics of induced systems and their enveloping semigroups. All the chapters in the book are well organized and systematically dealing with introductory topics through advanced research topics. The basic concepts give the motivation to begin with, then the theory, and finally the new research-oriented topics. The results are presented with detailed proof, plenty of examples and several open questions are put forward to motivate for future research. Some of the results, related to the enveloping semigroup, are new to the existing literature. The enveloping semigroups of the induced systems is considered for the first time in the literature, and some new results are obtained. The book has a research-oriented flavour in the field of topological dynamics.

Author : Fritz Colonius,Wolfgang Kliemann
Publisher : Unknown
Page : 302 pages
File Size : 45,6 Mb
Release : 2014
Category : Algebras, Linear
ISBN : 1470419327

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Dynamical Systems and Linear Algebra by Fritz Colonius,Wolfgang Kliemann Pdf

Author : Robert F. Brown
Publisher : Springer Science & Business Media
Page : 990 pages
File Size : 41,5 Mb
Release : 2005-07-21
Category : Mathematics
ISBN : 1402032218

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Handbook of Topological Fixed Point Theory by Robert F. Brown Pdf

This book will be especially useful for post-graduate students and researchers interested in the fixed point theory, particularly in topological methods in nonlinear analysis, differential equations and dynamical systems. The content is also likely to stimulate the interest of mathematical economists, population dynamics experts as well as theoretical physicists exploring the topological dynamics.

Author : Christopher Keil McCord
Publisher : American Mathematical Soc.
Page : 350 pages
File Size : 41,5 Mb
Release : 1993
Category : Mathematics
ISBN : 9780821851814

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Nielsen Theory and Dynamical Systems by Christopher Keil McCord Pdf

This volume contains the proceedings of the AMS-IMS-SIAM Joint Summer Research Conference on Nielsen Theory and Dynamical Systems, held in June 1992 at Mount Holyoke College. Focusing on the interface between Nielsen fixed point theory and dynamical systems, this book provides an almost complete survey of the state of the art of Nielsen theory. Most of the articles are expository, making them accessible to both graduate students and researchers in algebraic topology, fixed point theory, and dynamical systems.

Author : Thierry Giordano,David Kerr,N. Christopher Phillips,Andrew Toms
Publisher : Springer
Page : 498 pages
File Size : 52,5 Mb
Release : 2018-08-28
Category : Mathematics
ISBN : 9783319708690

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Crossed Products of C*-Algebras, Topological Dynamics, and Classification by Thierry Giordano,David Kerr,N. Christopher Phillips,Andrew Toms Pdf

This book collects the notes of the lectures given at an Advanced Course on Dynamical Systems at the Centre de Recerca Matemàtica (CRM) in Barcelona. The notes consist of four series of lectures. The first one, given by Andrew Toms, presents the basic properties of the Cuntz semigroup and its role in the classification program of simple, nuclear, separable C*-algebras. The second series of lectures, delivered by N. Christopher Phillips, serves as an introduction to group actions on C*-algebras and their crossed products, with emphasis on the simple case and when the crossed products are classifiable. The third one, given by David Kerr, treats various developments related to measure-theoretic and topological aspects of crossed products, focusing on internal and external approximation concepts, both for groups and C*-algebras. Finally, the last series of lectures, delivered by Thierry Giordano, is devoted to the theory of topological orbit equivalence, with particular attention to the classification of minimal actions by finitely generated abelian groups on the Cantor set.