Recurrence In Topological Dynamics
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Recurrence In Topological Dynamics
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Author : Ethan Akin
language : en
Publisher: Springer Science & Business Media
Release Date : 1997-07-31
Recurrence In Topological Dynamics written by Ethan Akin 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 1997-07-31 with Mathematics categories.
This groundbreaking volume is the first to elaborate the theory of set families as a tool for studying the phenomenon of recurrence. The theory is implicit in such seminal works as Hillel Furstenberg's Recurrence in Ergodic Theory and Combinational Number Theory, but Ethan Akin's study elaborates it in detail, defining such elements of theory as: open families of special subsets the unification of several ideas associated with transitivity, ergodicity, and mixing the Ellis theory of enveloping semigroups for compact dynamical systems and new notions of equicontinuity, distality, and rigidity.
Recurrence In Topological Dynamics
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Author : Ethan Akin
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09
Recurrence In Topological Dynamics written by Ethan Akin 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 2013-03-09 with Mathematics categories.
In the long run of a dynamical system, after transient phenomena have passed away, what remains is recurrence. An orbit is recurrent when it returns repeatedly to each neighborhood of its initial position. We can sharpen the concept by insisting that the returns occur with at least some prescribed frequency. For example, an orbit lies in some minimal subset if and only if it returns almost periodically to each neighborhood of the initial point. That is, each return time set is a so-called syndetic subset ofT= the positive reals (continuous time system) or T = the positive integers (discrete time system). This is a prototype for many of the results in this book. In particular, frequency is measured by membership in a family of subsets of the space modeling time, in this case the family of syndetic subsets of T. In applying dynamics to combinatorial number theory, Furstenberg introduced a large number of such families. Our first task is to describe explicitly the calculus of families implicit in Furstenberg's original work and in the results which have proliferated since. There are general constructions on families, e. g. , the dual of a family and the product of families. Other natural constructions arise from a topology or group action on the underlying set. The foundations are laid, in perhaps tedious detail, in Chapter 2. The family machinery is then applied in Chapters 3 and 4 to describe family versions of recurrence, topological transitivity, distality and rigidity.
Recurrence In Topological Dynamics
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Author : Ethan Akin
language : en
Publisher:
Release Date : 2014-01-15
Recurrence In Topological Dynamics written by Ethan Akin and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-01-15 with categories.
Recurrence And Topology
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Author : John M. Alongi
language : en
Publisher: American Mathematical Soc.
Release Date : 2007
Recurrence And Topology written by John M. Alongi 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 2007 with Mathematics categories.
Since at least the time of Poisson, mathematicians have pondered the notion of recurrence for differential equations. Solutions that exhibit recurrent behavior provide insight into the behavior of general solutions. In Recurrence and Topology, Alongi and Nelson provide a modern understanding of the subject, using the language and tools of dynamical systems and topology. Recurrence and Topology develops increasingly more general topological modes of recurrence for dynamical systems beginning with fixed points and concluding with chain recurrent points.
Recurrence In Ergodic Theory And Combinatorial Number Theory
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Author : Harry Furstenberg
language : en
Publisher: Princeton University Press
Release Date : 2014-07-14
Recurrence In Ergodic Theory And Combinatorial Number Theory written by Harry Furstenberg and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-07-14 with Mathematics categories.
Topological dynamics and ergodic theory usually have been treated independently. H. Furstenberg, instead, develops the common ground between them by applying the modern theory of dynamical systems to combinatories and number theory. Originally published in 1981. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.
The General Topology Of Dynamical Systems
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Author : Ethan Akin
language : en
Publisher: American Mathematical Soc.
Release Date : 1993
The General Topology Of Dynamical Systems written by Ethan Akin 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 1993 with Mathematics categories.
Recent work in dynamical systems theory has both highlighted certain topics in the pre-existing subject of topological dynamics (such as the construction of Lyapunov functions and various notions of stability) and also generated new concepts and results. This book collects these results, both old and new, and organises them into a natural foundation for all aspects of dynamical systems theory.
Topological Dynamics
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Author : Walter Helbig Gottschalk
language : en
Publisher: American Mathematical Soc.
Release Date : 1955-01-01
Topological Dynamics written by Walter Helbig Gottschalk 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 1955-01-01 with Mathematics categories.
Topological dynamics is the study of transformation groups with respect to those topological properties whose prototype occurred in classical dynamics. In this volume, Part One contains the general theory. Part Two contains notable examples of flows which have contributed to the general theory of topological dynamics and which have in turn have been illuminated by the general theory of topological dynamics.
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.
Topological Dynamics Of Enveloping Semigroups
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Author : Anima Nagar
language : en
Publisher: Springer Nature
Release Date : 2023-01-01
Topological Dynamics Of Enveloping Semigroups written by Anima Nagar and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-01-01 with Mathematics categories.
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.