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© 2018

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

Benefits

  • Features a unique, exhaustive list of results and methods concerning the Sarnak and Chowla conjectures

  • Includes a course in analytic number theory accessible to undergraduate students

  • Offers a clear presentation of the interaction of modern dynamics with number theory and combinatorics

Book

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

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

  • Book Title Ergodic Theory and Dynamical Systems in their Interactions with Arithmetics and Combinatorics
  • Book Subtitle CIRM Jean-Morlet Chair, Fall 2016
  • Editors Sébastien Ferenczi
    Joanna Kułaga-Przymus
    Mariusz Lemańczyk
  • Series Title Lecture Notes in Mathematics
  • Series Abbreviated Title Lect.Notes Mathematics
  • 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 Mathematics and Statistics (R0)
  • Softcover ISBN 978-3-319-74907-5
  • eBook ISBN 978-3-319-74908-2
  • Series ISSN 0075-8434
  • Series E-ISSN 1617-9692
  • Edition Number 1
  • Number of Pages IV, 434
  • Number of Illustrations 223 b/w illustrations, 8 illustrations in colour
  • Topics Dynamical Systems and Ergodic Theory
    Number Theory
    Combinatorics
    Geometry
  • Buy this book on publisher's site
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