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Ergodic Theory and Dynamical Systems in their Interactions with Arithmetics and Combinatorics

CIRM Jean-Morlet Chair, Fall 2016

  • Sébastien Ferenczi
  • Joanna Kułaga-Przymus
  • Mariusz Lemańczyk

Part of the Lecture Notes in Mathematics book series (LNM, volume 2213)

Table of contents

  1. Front Matter
    Pages i-xiv
  2. Part I

    1. Front Matter
      Pages 1-2
    2. Joël Rivat
      Pages 3-10
    3. Joël Rivat
      Pages 11-16
    4. Joël Rivat
      Pages 17-23
    5. Joël Rivat
      Pages 25-26
    6. Joël Rivat
      Pages 27-52
    7. Joël Rivat
      Pages 53-78
    8. Joël Rivat
      Pages 79-97
    9. Joël Rivat
      Pages 99-113
  3. Interactions Between Arithmetic and Dynamics

    1. Front Matter
      Pages 115-115
    2. M. Einsiedler, M. Luethi
      Pages 137-161
    3. Sébastien Ferenczi, Joanna Kułaga-Przymus, Mariusz Lemańczyk
      Pages 163-235
    4. Alexander Gomilko, Dominik Kwietniak, Mariusz Lemańczyk
      Pages 237-247
    5. Olivier Ramaré
      Pages 293-315
  4. Selected Topics in Dynamics

    1. Front Matter
      Pages 325-325
    2. Terrence Adams, Cesar E. Silva
      Pages 327-349
    3. Eli Glasner, Michael Megrelishvili
      Pages 351-392
  5. Back Matter
    Pages 433-434

About this book

Introduction

This book concentrates on the modern theory of dynamical systems and its interactions with number theory and combinatorics. The greater part begins with a course in analytic number theory and focuses on its links with ergodic theory, presenting an exhaustive account of recent research on Sarnak's conjecture on Möbius disjointness. Selected topics involving more traditional connections between number theory and dynamics are also presented, including equidistribution, homogenous dynamics, and Lagrange and Markov spectra. In addition, some dynamical and number theoretical aspects of aperiodic order, some algebraic systems, and a recent development concerning tame systems are described.

Keywords

Analytic Number Theory Ergodic Theory Equidistribution Homogenous Dynamics Lagrange Spectrum Moebius Disjointness Multiplicative Functions Sarnak's Conjecture Chowla's Conjecture Translation Surfaces

Editors and affiliations

  • Sébastien Ferenczi
    • 1
  • Joanna Kułaga-Przymus
    • 2
  • Mariusz Lemańczyk
    • 3
  1. 1.CNRS UMR 7373Institut de Mathématiques de MarseilleMarseilleFrance
  2. 2.Faculty of Mathematics and Computer ScienceNicolaus Copernicus UniversityToruńPoland
  3. 3.Faculty of Mathematics and Computer ScienceNicolaus Copernicus UniversityToruńPoland

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-74908-2
  • Copyright Information Springer International Publishing AG, part of Springer Nature 2018
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-74907-5
  • Online ISBN 978-3-319-74908-2
  • Series Print ISSN 0075-8434
  • Series Online ISSN 1617-9692
  • Buy this book on publisher's site