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Author: Fabien Durand
Publisher: Cambridge University Press
Published: 2022-02-03
Total Pages: 593
ISBN-13: 1108838685
DOWNLOAD EBOOKThis is the first self-contained exposition of the connections between symbolic dynamical systems, dimension groups and Bratteli diagrams.
Author: Fabien Durand
Publisher: Cambridge University Press
Published: 2022-02-03
Total Pages: 594
ISBN-13: 1108986099
DOWNLOAD EBOOKThis 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.
Author: Michel Coornaert
Publisher:
Published: 2015
Total Pages:
ISBN-13: 9783319197951
DOWNLOAD EBOOKTranslated 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.
Author: E. H. Dowell
Publisher: World Scientific
Published: 2003
Total Pages: 288
ISBN-13: 9789812384676
DOWNLOAD EBOOKMany books on dynamics start with a discussion of systems with one or two degrees of freedom and then turn to the generalization to the case of many degrees of freedom. For linear systems, the concept of eigenfunctions provides a compact and elegant method for decomposing the dynamics of a high dimensional system into a series of independent single-degree-of-freedom dynamical systems. Yet, when the system has a very high dimension, the determination of the eigenfunctions may be a distinct challenge, and when the dynamical system is nonconservative and/or nonlinear, the whole notion of uncoupled eigenmodes requires nontrivial extensions of classical methods. These issues constitute the subject of this book.
Author: Ya. B. Pesin
Publisher: University of Chicago Press
Published: 1997
Total Pages: 326
ISBN-13: 9780226662213
DOWNLOAD EBOOKIn this book, Yakov B. 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. Topics include, but are not restricted to, the general concept of dimension; the dimension interpretation of some well-known invariants of dynamical systems, such as topological and measure-theoretic entropies; formulas of dimension of some well-known hyperbolic invariant sets, such as Julia sets, horseshoes, and solenoids; mathematical analysis of dimensions that are most often used in applied research, such as correlation and information dimensions; and mathematical theory of invariant multifractals. 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. The book can also be used as a text for a special topics course in the theory of dynamical systems and dimension theory.
Author: Nikolay Kuznetsov
Publisher: Springer Nature
Published: 2020-07-02
Total Pages: 555
ISBN-13: 3030509877
DOWNLOAD EBOOKThis book provides analytical and numerical methods for the estimation of dimension characteristics (Hausdorff, Fractal, Carathéodory dimensions) for attractors and invariant sets of dynamical systems and cocycles generated by smooth differential equations or maps in finite-dimensional Euclidean spaces or on manifolds. It also discusses stability investigations using estimates based on Lyapunov functions and adapted metrics. Moreover, it introduces various types of Lyapunov dimensions of dynamical systems with respect to an invariant set, based on local, global and uniform Lyapunov exponents, and derives analytical formulas for the Lyapunov dimension of the attractors of the Hénon and Lorenz systems. Lastly, the book presents estimates of the topological entropy for general dynamical systems in metric spaces and estimates of the topological dimension for orbit closures of almost periodic solutions to differential equations.
Author: B. Hasselblatt
Publisher: Elsevier
Published: 2002
Total Pages: 1244
ISBN-13:
DOWNLOAD EBOOKThis second half of Volume 1 of this Handbook follows Volume 1A, which was published in 2002. The contents of these two tightly integrated parts taken together come close to a realization of the program formulated in the introductory survey "Principal Structures” of Volume 1A. The present volume contains surveys on subjects in four areas of dynamical systems: Hyperbolic dynamics, parabolic dynamics, ergodic theory and infinite-dimensional dynamical systems (partial differential equations). . Written by experts in the field. . The coverage of ergodic theory in these two parts of Volume 1 is considerably more broad and thorough than that provided in other existing sources. . The final cluster of chapters discusses partial differential equations from the point of view of dynamical systems.
Author: V.I. Arnol'd
Publisher: Springer Science & Business Media
Published: 1993-12-06
Total Pages: 360
ISBN-13: 9783540181767
DOWNLOAD EBOOKA collection of five surveys on dynamical systems, indispensable for graduate students and researchers in mathematics and theoretical physics. Written in the modern language of differential geometry, the book covers all the new differential geometric and Lie-algebraic methods currently used in the theory of integrable systems.
Author: Michael Brin
Publisher: Cambridge University Press
Published: 2004-08-16
Total Pages: 490
ISBN-13: 9780521840736
DOWNLOAD EBOOKThis volume presents a broad collection of current research by leading experts in the theory of dynamical systems.
Author: Roger Temam
Publisher: Springer Science & Business Media
Published: 2012-12-06
Total Pages: 517
ISBN-13: 1468403133
DOWNLOAD EBOOKThis is the first attempt at a systematic study of infinite dimensional dynamical systems generated by dissipative evolution partial differential equations arising in mechanics and physics. Other areas of science and technology are included where appropriate. The relation between infinite and finite dimensional systems is presented from a synthetic viewpoint and equations considered include reaction-diffusion, Navier-Stokes and other fluid mechanics equations, magnetohydrodynamics, thermohydraulics, pattern formation, Ginzburg-Landau, damped wave and an introduction to inertial manifolds.
