Ergodic Theory and Dynamical Systems in their Interactions with Arithmetics and Combinatorics : CIRM Jean-Morlet Chair, Fall 2016 / edited by Sébastien Ferenczi, Joanna Kułaga-Przymus, Mariusz Lemańczyk.

Format:

Book

Contributor:

Ferenczi, Sébastien, editor.

Kułaga-Przymus, Joanna, editor.

Lemańczyk, Mariusz, editor.

SpringerLink (Online service)

Series:

Lecture Notes in Mathematics, 0075-8434 ; 2213.

Lecture Notes in Mathematics, 0075-8434 ; 2213

Language:

English

Subjects (All):

Differentiable dynamical systems.

Number theory.

Combinatorial analysis.

Geometry.

Dynamical Systems and Ergodic Theory.

Number Theory.

Combinatorics.

Local Subjects:

Dynamical Systems and Ergodic Theory.

Number Theory.

Combinatorics.

Geometry.

Physical Description:

1 online resource (IV, 434 pages) : 231 illustrations, 8 illustrations in color.

Contained In:

Springer eBooks

Place of Publication:

Cham : Springer International Publishing : Imprint: Springer, 2018.

System Details:

text file PDF

Summary:

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.

Contents:

Part I. Bases of Analytic Number Theory

1. Prime Numbers

2. Arithmetic Functions

3. Dirichlet Series

4. Euler's Gamma Function

5. Riemann's Zeta Function

6. The Large Sieve

7. The Theorem of Vinogradov

8. The van der Corput Method.- Part II. Interactions Between Arithmetics and Dynamics

9. A Brief Guide to Reversing and Extended Symmetries of Dynamical Systems

10. Kloosterman Sums, Disjointness, and Equidistribution

11. Sarnak's Conjecture - what's new

12. Sarnak's Conjecture Implies the Chowla Conjecture Along a Subsequence

13. On the Logarithmic Probability that a Random Integral Ideal is A-free

14. The Lagrange and Markov Spectra from the Dynamical Point of View

15. On the missing Log Factor

16. Chowla's Conjecture: From the Liouville Function to the Moebius Function.- Part III. Selected Topics in Dynamics

17. Weak Mixing for Infinite Measure Invertible Transformations

18. More on Tame Dynamical Systems

19. A Piecewise Rotation of the Circle, IPR Maps and Their Connection with Translation Surfaces.

Other Format:

Printed edition:

ISBN:

9783319749082

Access Restriction:

Restricted for use by site license.