Recurrence in Topological Dynamics: Furstenberg Families and Ellis Actions

Hardcover | July 31, 1997

byEthan Akin

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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.

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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 element...

Format:HardcoverDimensions:276 pages, 9.25 × 6.1 × 0.04 inPublished:July 31, 1997Publisher:Springer US

The following ISBNs are associated with this title:

ISBN - 10:0306455501

ISBN - 13:9780306455506

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Table of Contents

Monoid Actions. Furstenberg Families. Recurrence. Transitive and Central Systems. Compactifications. Ellis Semigroups and Ellis Actions. Semigroups and Families. Equicontinuity. Appendix: Semicontinuous Relations and Almost Open Maps. Index.