**Contemporary Mathematics**

Volume: 532;
2010;
242 pp;
Softcover

MSC: Primary 11; 20; 22; 30; 37; 54; 60;

Print ISBN: 978-0-8218-4958-3

Product Code: CONM/532

List Price: $83.00

Individual Member Price: $66.40

**Electronic ISBN: 978-0-8218-8211-5
Product Code: CONM/532.E**

List Price: $83.00

Individual Member Price: $66.40

# Dynamical Numbers: Interplay between Dynamical Systems and Number Theory

Share this page *Edited by *
*Sergiy Kolyada; Yuri Manin; Martin Möller; Pieter Moree; Thomas Ward*

This volume contains papers from the special program and international
conference on Dynamical Numbers which were held at the Max-Planck
Institute in Bonn, Germany in 2009.

These papers reflect the extraordinary range and depth of the interactions
between ergodic theory and dynamical systems and number theory. Topics
covered in the book include stationary measures, systems of enumeration,
geometrical methods, spectral methods, and algebraic dynamical systems.

#### Readership

Graduate students and research mathematicians interested in ergodic theory, dynamical systems, and number theory.

# Table of Contents

## Dynamical Numbers: Interplay between Dynamical Systems and Number Theory

- Contents v6 free
- Preface vii8 free
- List of Participants ix10 free
- Stationary dynamical systems 114 free
- Introduction 114
- 1. Stationary dynamical systems 215
- 2. Examples 518
- 3. Joinings 821
- 4. A structure theorem for stationary systems 922
- 5. A Nevo-Zimmer type theorem in an abstract setup 1528
- 6. A Szemerédi type theorem for SL(2,R). 1730
- 7. WAP actions are stiff 2134
- 8. The SAT property 2235
- References 2740

- Geodesic flow on the Teichmüller disk of the regular octagon, cutting sequences and octagon continued fractions maps 2942
- Expansion of rational numbers in Möbius number systems 6780
- Localisation of algebraic integers and polynomial iteration 8396
- Horospheres and Farey fractions 97110
- Exponential mixing for automorphisms on compact Kähler manifolds 107120
- Orbit theory, locally finite permutations and Morse arithmetic 115128
- Ergodic abelian actions with homogeneous spectrum 137150
- Geometric entropy of geodesic currents on free groups 149162
- Laurent polynomial moment problem: A case study 177190
- Entropy and growth rate of periodic points of algebraic Zd-actions 195208
- Statistics of matrix products in hyperbolic geometry 213226
- Infinite sequence of fixed point free pseudo-Anosov homeomorphisms on a family of genus two surface 149162