Topological Theory of Dynamical Systems

Recent Advances

Author: N. Aoki,K. Hiraide

Publisher: Elsevier

ISBN: 9780080887210

Category: Mathematics

Page: 415

View: 5368

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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.

Simplicial Dynamical Systems

Author: Ethan Akin

Publisher: American Mathematical Soc.

ISBN: 0821813838

Category: Mathematics

Page: 197

View: 648

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Abstract A - simplicial dynamical system is a simplicial map $g:K^* \rightarrow K$ where $K$ is a finite simplicial complex triangulating a compact polyhedron $X$ and $K^*$ is a proper subdivision of $K$, e.g. the barycentric or any further subdivision. The dynamics of the associated piecewise linear map $g: X X$ can be analyzed by using certain naturally related subshifts of finite type. Any continuous map on $X$ can be $C^0$ approximated by such systems. Other examples yield interesting subshift constructions.

Encyclopedia of General Topology

Author: K.P. Hart,Jun-iti Nagata,J.E. Vaughan

Publisher: Elsevier

ISBN: 9780080530864

Category: Mathematics

Page: 536

View: 1213

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This book is designed for the reader who wants to get a general view of the terminology of General Topology with minimal time and effort. The reader, whom we assume to have only a rudimentary knowledge of set theory, algebra and analysis, will be able to find what they want if they will properly use the index. However, this book contains very few proofs and the reader who wants to study more systematically will find sufficiently many references in the book. Key features: • More terms from General Topology than any other book ever published • Short and informative articles • Authors include the majority of top researchers in the field • Extensive indexing of terms

Shadowing in Dynamical Systems

Theory and Applications

Author: K.J. Palmer

Publisher: Springer Science & Business Media

ISBN: 9780792361794

Category: Mathematics

Page: 300

View: 9691

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In this book the theory of hyperbolic sets is developed, both for diffeomorphisms and flows, with an emphasis on shadowing. We show that hyperbolic sets are expansive and have the shadowing property. Then we use shadowing to prove that hyperbolic sets are robust under perturbation, that they have an asymptotic phase property and also that the dynamics near a transversal homoclinic orbit is chaotic. It turns out that chaotic dynamical systems arising in practice are not quite hyperbolic. However, they possess enough hyperbolicity to enable us to use shadowing ideas to give computer-assisted proofs that computed orbits of such systems can be shadowed by true orbits for long periods of time, that they possess periodic orbits of long periods and that it is really true that they are chaotic. Audience: This book is intended primarily for research workers in dynamical systems but could also be used in an advanced graduate course taken by students familiar with calculus in Banach spaces and with the basic existence theory for ordinary differential equations.

Topological Dynamics of Random Dynamical Systems

Author: Nguyen Dinh Cong

Publisher: Oxford University Press

ISBN: 9780198501572

Category: Mathematics

Page: 203

View: 6418

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This book is a systematic presentation of the solution of one of the fundamental problems of the theory of random dynamical systems - the problem of topological classification and structural stability of linear hyperbolic random dynamical systems. Employing the tools and methods of algebraic ergodic theory, the theory presented in the book has surprisingly beautiful results showing the richness of random dynamical systems as well as giving a gentle generalizationof the classical deterministic theory.

Invitation to C*-algebras and Topological Dynamics

Author: Jun Tomiyama

Publisher: World Scientific

ISBN: 9789971503383

Category: Science

Page: 167

View: 7026

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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.

Descriptive Set Theory and Dynamical Systems

Author: M. Foreman,A. S. Kechris,A. Louveau,B. Weiss

Publisher: Cambridge University Press

ISBN: 9780521786447

Category: Mathematics

Page: 291

View: 1010

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In recent years there has been a growing interest in the interactions between descriptive set theory and various aspects of the theory of dynamical systems, including ergodic theory and topological dynamics. This volume, first published in 2000, contains a collection of survey papers by leading researchers covering a wide variety of recent developments in these subjects and their interconnections. This book provides researchers and graduate students interested in either of these areas with a guide to work done in the other, as well as with an introduction to problems and research directions arising from their interconnections.

The Analytical and Topological Theory of Semigroups

Trends and Developments

Author: Karl H. Hofmann,Jimmie D. Lawson,John S. Pym

Publisher: Walter de Gruyter

ISBN: 3110856042

Category: Mathematics

Page: 409

View: 8732

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The aim of the series is to present new and important developments in pure and applied mathematics. Well established in the community over two decades, it offers a large library of mathematics including several important classics. The volumes supply thorough and detailed expositions of the methods and ideas essential to the topics in question. In addition, they convey their relationships to other parts of mathematics. The series is addressed to advanced readers wishing to thoroughly study the topic. Editorial Board Lev Birbrair, Universidade Federal do Ceará, Fortaleza, Brasil Victor P. Maslov, Russian Academy of Sciences, Moscow, Russia Walter D. Neumann, Columbia University, New York, USA Markus J. Pflaum, University of Colorado, Boulder, USA Dierk Schleicher, Jacobs University, Bremen, Germany

Recent Progress in General Topology III

Author: K.P. Hart,J. van Mill,P. Simon

Publisher: Springer Science & Business Media

ISBN: 946239024X

Category: Mathematics

Page: 903

View: 7138

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The book presents surveys describing recent developments in most of the primary subfields of General Topology, and its applications to Algebra and Analysis during the last decade, following the previous editions (North Holland, 1992 and 2002). The book was prepared in connection with the Prague Topological Symposium, held in 2011. During the last 10 years the focus in General Topology changed and therefore the selection of topics differs from that chosen in 2002. The following areas experienced significant developments: Fractals, Coarse Geometry/Topology, Dimension Theory, Set Theoretic Topology and Dynamical Systems.

DCDS-A

Author: N.A

Publisher: N.A

ISBN: N.A

Category: Mathematics

Page: N.A

View: 2011

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Ergodic Theory and Dynamical Systems in their Interactions with Arithmetics and Combinatorics

CIRM Jean-Morlet Chair, Fall 2016

Author: Sébastien Ferenczi,Joanna Kułaga-Przymus,Mariusz Lemańczyk

Publisher: Springer

ISBN: 3319749080

Category: Mathematics

Page: 434

View: 9427

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This book concentrates on the modern theory of dynamical systems and its interactions with number theory and combinatorics. The greater part begins with a course in analytic number theory and focuses on its links with ergodic theory, presenting an exhaustive account of recent research on Sarnak's conjecture on Möbius disjointness. Selected topics involving more traditional connections between number theory and dynamics are also presented, including equidistribution, homogenous dynamics, and Lagrange and Markov spectra. In addition, some dynamical and number theoretical aspects of aperiodic order, some algebraic systems, and a recent development concerning tame systems are described.

Topological Dynamical Systems

An Introduction to the Dynamics of Continuous Mappings

Author: Jan Vries

Publisher: Walter de Gruyter GmbH & Co KG

ISBN: 3110374595

Category: Mathematics

Page: 513

View: 1309

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This book is an elementary introduction to the theory of discrete dynamical systems, also stressing the topological background of the topic. It treats all important concepts needed to understand recent literature from the 'applied general topology' angle. The book is addressed to graduate students and beyond.