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

CIRM Jean-Morlet Chair, Fall 2016

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  • © 2018

Overview

  • 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

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

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About this book

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.

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Keywords

Table of contents (19 chapters)

  1. Part I

  2. Interactions Between Arithmetic and Dynamics

  3. Selected Topics in Dynamics

Editors and Affiliations

  • CNRS UMR 7373, Institut de Mathématiques de Marseille, Marseille, France

    Sébastien Ferenczi

  • Faculty of Mathematics and Computer Science, Nicolaus Copernicus University, Toruń, Poland

    Joanna Kułaga-Przymus, Mariusz Lemańczyk

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

  • DOI: https://doi.org/10.1007/978-3-319-74908-2

  • Publisher: Springer Cham

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: Springer International Publishing AG, part of Springer Nature 2018

  • Softcover ISBN: 978-3-319-74907-5Published: 16 June 2018

  • eBook ISBN: 978-3-319-74908-2Published: 15 June 2018

  • 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

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