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Topics in Dynamics and Ergodic Theory

$61.00 ( ) USD

Part of London Mathematical Society Lecture Note Series

  • Editors:
  • Sergey Bezuglyi, Institute of Low-Temperature Physics and Engineering, Kharkov, Ukraine
  • Sergiy Kolyada, National Academy of Sciences of Ukraine
Anatole M. Stepin, Vitaly Bergelson, André de Carvalho, Toby Hall, Anthony H. Dooley, Vladim Kaloshin, Oleg Kozlovski, Bas Lemmens, Nikita Sidorov, Klaus Thomsen, Benjamin Weiss
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  • Date Published: December 2004
  • availability: This ISBN is for an eBook version which is distributed on our behalf by a third party.
  • format: Adobe eBook Reader
  • isbn: 9780511059254

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About the Authors
  • This collection of survey papers by leading researchers in ergodic theory and low-dimensional and topological dynamics comprises nine chapters on a range of important topics. These include: the role and usefulness of ultrafilters in ergodic theory, topological dynamics and Ramsey theory; topological aspects of kneading theory together with an analogous 2-dimensional theory called pruning; the dynamics of Markov odometers, Bratteli-Vershik diagrams and orbit equivalence of non-singular automorphisms; geometric proofs of Mather's connecting and accelerating theorems; recent results in one dimensional smooth dynamics; periodic points of nonexpansive maps; arithmetic dynamics; the defect of factor maps; entropy theory for actions of countable amenable groups.

    • Contains survey articles addressed to a wide range of mathematicians
    • Nice, detailed exposition of new ideas and results
    • The reader has an opportunity to become acquainted with new directions in ergodic theory, topological and symbolic dynamics
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    Product details

    • Date Published: December 2004
    • format: Adobe eBook Reader
    • isbn: 9780511059254
    • contains: 23 b/w illus. 4 tables 20 exercises
    • availability: This ISBN is for an eBook version which is distributed on our behalf by a third party.
  • Table of Contents

    1. Introductory talk at the opening of the conference Anatole M. Stepin
    2. Minimal idempotents and ergodic Ramsey theory Vitaly Bergelson
    3. Symbolic dynamics and topological models in dimensions 1 and 2 André de Carvalho and Toby Hall
    4. Markov odometers Anthony H. Dooley
    5. Geometric proofs of Mather's connecting and accelerating theorems Vadim Kaloshin
    6. Structural stability in one dimensional dynamics Oleg Kozlovski
    7. Periodic points of nonexpansive maps: a survey Bas Lemmens
    8. Arithmetic dynamics Nikita Sidorov
    9. The defect of factor maps and finite equivalence of dynamical systems Klaus Thomsen
    10. Actions of amenable groups Benjamin Weiss.

  • Editors

    Sergey Bezuglyi, Institute of Low-Temperature Physics and Engineering, Kharkov, Ukraine

    Sergiy Kolyada, National Academy of Sciences of Ukraine

    Contributors

    Anatole M. Stepin, Vitaly Bergelson, André de Carvalho, Toby Hall, Anthony H. Dooley, Vladim Kaloshin, Oleg Kozlovski, Bas Lemmens, Nikita Sidorov, Klaus Thomsen, Benjamin Weiss

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