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Recurrence in Topological Dynamics: Furstenberg Families and Ellis Actions (University Series in Mathematics) download epub

by Ethan Akin


Epub Book: 1432 kb. | Fb2 Book: 1651 kb.

Recurrence in Topological. has been added to your Cart. Series: University Series in Mathematics. Hardcover: 266 pages.

Recurrence in Topological.

University Series in Mathematics. Furstenberg Families. Recurrence in Topological Dynamics. Furstenberg Families and Ellis Actions. Authors: Akin, Ethan.

Recurrence in Topological Dynamics book. In the long run of a dynamical system, after transient.

Recurrence in topological dynamics: Furstenberg families and Ellis actions. We use this to prove that every monothetic group has an action which is weak mixing and topologically ergodic. The General Topology of Dynamical Systems.

oceedings{Akin2003TheTD, title {The Topological Dynamics of Ellis Actions}, author {Ethan Akin and Joseph Auslander and Eli Glasner}, year . Will Brian, Piotr Oprocha.

oceedings{Akin2003TheTD, title {The Topological Dynamics of Ellis Actions}, author {Ethan Akin and Joseph Auslander and Eli Glasner}, year {2003} }. Ethan Akin, Joseph Auslander, Eli Glasner. Introduction Semigroups, monoids and their actions Ellis semigroups and Ellis actions Continuity conditions Applications using ideals Classical dynamical systems Classical actions: The group case Classical actions: The Abelian case Iterations of continuous maps Table Bibliography Index.

Recurrence in Topological Dynamics: Furstenberg Families and Ellis Actions (University Series in Mathematics). Plenum Press, New York, 1997. Lectures on Cantor and Mycielski sets for dynamical systems. Minimal Flows and Their Extensions. North Holland, Amsterdam, 1988. Ellis groups of quasi-factors of minimal flow.

Akin, Recurrence in Topological Dynamics, Furstenberg Families and Ellis Actions,, The University Series in Mathematics, (1997). E. Akin, Lectures on Cantor and Mycielski sets for dynamical systems,, in Chapel Hill Ergodic Theory Workshops, (2004), 21. doi: 1. 090/conm/356/06496.

Furstenberg Families and Sensitivity. Huoyun Wang,1 Jincheng Xiong,2 and Feng Tan2. 1Department of Mathematics, Guangzhou University, Guangzhou 510006, China 2Department of Mathematics, South China Normal University, Guangzhou 526061, China. Received 31 August 2009; Revised 17 November 2009; Accepted 22 January 2010.

North Academic Center 6/287A. Below I have posted pdf files of some introductory material describing two books, "The General Topology of Dynamical Systems" (1993) and "Recurrence in Topological Dynamics: Furstenberg Families and Ellis Actions" (1997) as well as two monographs "Simplicial Dynamical Systems" (1999) and "Dynamics of Topologically Generic Homeomorphisms" (2003). The survey of topological dynamics is my - rather idiosyncratic - view of the subject. It is in the Encyclopedia of Complexity and Systems Science (2009).

E. Akin, Recurrence in topological dynamics. Furstenberg families and Ellis actions, The University Series in Mathematics, Plenum Press, New York (1997). J. Banks, J. Brooks, G. Cairns, G. Davis, P. Stacey, On Devaney’s definition of chaos, Amer. Monthly, 99 (1992), 332–334. S. Cánovas, Li-Yorke chaos in a class of nonautonomous discrete systems, J. Difference Equ. Appl.

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: Furstenberg Families and Ellis Actions (University Series in Mathematics) download epub
Mathematics
Author: Ethan Akin
ISBN: 0306455501
Category: Science & Math
Subcategory: Mathematics
Language: English
Publisher: Springer; 1997 edition (July 31, 1997)
Pages: 266 pages