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Dimension Groups and Dynamical Systems

2022-02-03 Mathematics
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Release : 2022-02-03
Genre : Mathematics
Kind : eBook
Book Rating : 099/5 ( reviews)

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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. This book was released on 2022-02-03. 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.

Topological Dimension and Dynamical Systems

2015
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Release : 2015
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Kind : eBook
Book Rating : 951/5 ( reviews)

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Book Synopsis Topological Dimension and Dynamical Systems by : Michel Coornaert

Download or read book Topological Dimension and Dynamical Systems written by Michel Coornaert. This book was released on 2015. 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.

Infinite-Dimensional Dynamical Systems in Mechanics and Physics

2013-12-11 Mathematics
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Release : 2013-12-11
Genre : Mathematics
Kind : eBook
Book Rating : 456/5 ( reviews)

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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. This book was released on 2013-12-11. 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.

Groups and Graphs, Designs and Dynamics

2024-05-30 Mathematics
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Release : 2024-05-30
Genre : Mathematics
Kind : eBook
Book Rating : 945/5 ( reviews)

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Book Synopsis Groups and Graphs, Designs and Dynamics by : R. A. Bailey

Download or read book Groups and Graphs, Designs and Dynamics written by R. A. Bailey. This book was released on 2024-05-30. Available in PDF, EPUB and Kindle. Book excerpt: This collection of four short courses looks at group representations, graph spectra, statistical optimality, and symbolic dynamics, highlighting their common roots in linear algebra. It leads students from the very beginnings in linear algebra to high-level applications: representations of finite groups, leading to probability models and harmonic analysis; eigenvalues of growing graphs from quantum probability techniques; statistical optimality of designs from Laplacian eigenvalues of graphs; and symbolic dynamics, applying matrix stability and K-theory. An invaluable resource for researchers and beginning Ph.D. students, this book includes copious exercises, notes, and references.

Dimension Theory in Dynamical Systems

2008-04-15 Mathematics
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Release : 2008-04-15
Genre : Mathematics
Kind : eBook
Book Rating : 233/5 ( reviews)

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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. This book was released on 2008-04-15. 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.

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