Topological Dynamics And Applications
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Topological Dynamics And Applications
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Author : Robert Ellis
language : en
Publisher: American Mathematical Soc.
Release Date : 1998
Topological Dynamics And Applications written by Robert Ellis and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998 with Mathematics categories.
This book is a very readable exposition of the modern theory of topological dynamics and presents diverse applications to such areas as ergodic theory, combinatorial number theory and differential equations. There are three parts: 1) The abstract theory of topological dynamics is discussed, including a comprehensive survey by Furstenberg and Glasner on the work and influence of R. Ellis. Presented in book form for the first time are new topics in the theory of dynamical systems, such as weak almost-periodicity, hidden eigenvalues, a natural family of factors and topological analogues of ergodic decomposition. 2) The power of abstract techniques is demonstrated by giving a very wide range of applications to areas of ergodic theory, combinatorial number theory, random walks on groups and others. 3) Applications to non-autonomous linear differential equations are shown. Exposition on recent results about Floquet theory, bifurcation theory and Lyapanov exponents is given.
Topological Dynamics And Applications
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Author :
language : en
Publisher: American Mathematical Soc.
Release Date : 1998
Topological Dynamics And Applications written by and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998 with Topological dynamics categories.
Advances In Topology Dynamical Systems And Interdisciplinary Applications
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Author : Bipan Hazarika
language : en
Publisher: Springer Nature
Release Date : 2025-06-04
Advances In Topology Dynamical Systems And Interdisciplinary Applications written by Bipan Hazarika and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-06-04 with Mathematics categories.
This book contains selected chapters on topology and dynamical systems and their interdisciplinary applications. Targeting researchers in interdisciplinary areas, the book covers contemporary interdisciplinary topics in topology and dynamical systems, such as closure functions, Partially Negative Dimensional Product (PNDP) manifolds, Khalimsky topological subspaces, neutrosophic topological space, ideal topological spaces, relator spaces, predator–prey symbiosis, cosmological models, and nanofluids.
Elements Of Topological Dynamics
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Author : J. de Vries
language : en
Publisher: Springer Science & Business Media
Release Date : 1993-06-30
Elements Of Topological Dynamics written by J. de Vries and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993-06-30 with Mathematics categories.
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.
Algebraic And Topological Dynamics
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Author : S. F. Koli︠a︡da
language : en
Publisher: American Mathematical Soc.
Release Date : 2005
Algebraic And Topological Dynamics written by S. F. Koli︠a︡da and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with Mathematics categories.
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, statisticalproperties of dynamical systems, and the theory of entropy and chaos. The book is suitable for graduate students and researchers interested in dynamical systems.
Topological Dynamical Systems
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Author : Jan Vries
language : en
Publisher: Walter de Gruyter
Release Date : 2014-01-31
Topological Dynamical Systems written by Jan Vries and has been published by Walter de Gruyter this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-01-31 with Mathematics categories.
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.
Handbook Of Dynamical Systems
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Author : A. Katok
language : en
Publisher: Elsevier
Release Date : 2005-12-17
Handbook Of Dynamical Systems written by A. Katok and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-12-17 with Mathematics categories.
This 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.
Elements Of Topological Dynamics
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Author : J. de Vries
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-17
Elements Of Topological Dynamics written by J. de Vries and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-04-17 with Mathematics categories.
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.
Lectures On Dynamical Systems Structural Stability And Their Applications
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Author : Kotik K Lee
language : en
Publisher: World Scientific
Release Date : 1992-05-14
Lectures On Dynamical Systems Structural Stability And Their Applications written by Kotik K Lee and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992-05-14 with Mathematics categories.
The communication of knowledge on nonlinear dynamical systems, between the mathematicians working on the analytic approach and the scientists working mostly on the applications and numerical simulations has been less than ideal. This volume hopes to bridge the gap between books written on the subject by mathematicians and those written by scientists. The second objective of this volume is to draw attention to the need for cross-fertilization of knowledge between the physical and biological scientists. The third aim is to provide the reader with a personal guide on the study of global nonlinear dynamical systems.
Topological And Ergodic Theory Of Symbolic Dynamics
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Author : Henk Bruin
language : en
Publisher: American Mathematical Society
Release Date : 2023-01-20
Topological And Ergodic Theory Of Symbolic Dynamics written by Henk Bruin and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-01-20 with Mathematics categories.
Symbolic dynamics is essential in the study of dynamical systems of various types and is connected to many other fields such as stochastic processes, ergodic theory, representation of numbers, information and coding, etc. This graduate text introduces symbolic dynamics from a perspective of topological dynamical systems and presents a vast variety of important examples. After introducing symbolic and topological dynamics, the core of the book consists of discussions of various subshifts of positive entropy, of zero entropy, other non-shift minimal action on the Cantor set, and a study of the ergodic properties of these systems. The author presents recent developments such as spacing shifts, square-free shifts, density shifts, $mathcal{B}$-free shifts, Bratteli-Vershik systems, enumeration scales, amorphic complexity, and a modern and complete treatment of kneading theory. Later, he provides an overview of automata and linguistic complexity (Chomsky's hierarchy). The necessary background for the book varies, but for most of it a solid knowledge of real analysis and linear algebra and first courses in probability and measure theory, metric spaces, number theory, topology, and set theory suffice. Most of the exercises have solutions in the back of the book.