**Contemporary Mathematics**

Volume: 631;
2015;
258 pp;
Softcover

MSC: Primary 22; 28; 37; 60;

Print ISBN: 978-1-4704-0931-9

Product Code: CONM/631

List Price: $105.00

AMS Member Price: $84.00

MAA member Price: $94.50

**Electronic ISBN: 978-1-4704-2219-6
Product Code: CONM/631.E**

List Price: $105.00

AMS Member Price: $84.00

MAA member Price: $94.50

# Recent Trends in Ergodic Theory and Dynamical Systems

Share this page *Edited by *
*Siddhartha Bhattacharya; Tarun Das; Anish Ghosh; Riddhi Shah*

This volume contains the proceedings of the International Conference
on Recent Trends in Ergodic Theory and Dynamical Systems, in honor of
S. G. Dani's 65th Birthday, held December 26–29, 2012, in Vadodara,
India.

This volume covers many topics of ergodic theory, dynamical
systems, number theory and probability measures on groups. Included
are papers on Teichmüller dynamics, Diophantine approximation,
iterated function systems, random walks and algebraic dynamical
systems, as well as two surveys on the work of S. G. Dani.

#### Readership

Graduate students and research mathematicians interested in ergodic theory and dynamics systems and their applications.

# Table of Contents

## Recent Trends in Ergodic Theory and Dynamical Systems

- Cover Cover11 free
- Title page iii4 free
- Contents vii8 free
- Preface ix10 free
- S. G. Dani as I have known him 112 free
- Cubic averages and large intersections 516
- Liouville property on 𝐺-spaces 2132
- A new connection between metric theory of Diophantine approximations and distribution of algebraic numbers 3344
- 1. Introduction 3344
- 2. Effective theorems in metric theory of Diophantine approximations of dependent variables 3546
- 3. Distribution of conjugate algebraic numbers 3748
- 4. Distribution of resultants of integral polynomials 3950
- 5. Distribution of discriminants of integral polynomials 4051
- 6. Algebraic numbers in small intervals 4253
- References 4253

- The gap distribution of slopes on the golden L 4758
- 1. Introduction 4758
- 2. Strata, \SL(2,\R)-action, and Veech groups 5061
- 3. Horocycle flows and first return maps 5263
- 4. Ergodicity and equidistribution 5566
- 5. Further questions 5768
- A. Explicit formulas for the probability distribution function 5869
- B. Volume computations 5869
- C. Quadratic Asymptotics 6071
- References 6172

- Uniformly recurrent subgroups 6374
- Values of binary quadratic forms at integer points and Schmidt games 7788
- Conformal families of measures for general iterated function systems 93104
- Dani’s work on probability measures on groups 109120
- 1. Introduction to the embedding problem 109120
- 2. The embedding problem on connected Lie groups 110121
- 3. A basic technique and its applications 111122
- 4. Recent results on the embedding problem on Lie groups 114125
- 5. The embedding problem on general locally compact groups 114125
- References 115126

- On the homogeneity at infinity of the stationary probability for an affine random walk 119130
- Dani’s work on dynamical systems on homogeneous spaces 131142
- Calculus of generalized Riesz products 145156
- 1. Introduction 145156
- 2. Generalized Riesz Products and their Weak Dichotomy 149160
- 3. Outer Polynomials and Mahler Measure 154165
- 4. A Formula for Radon Nikodym Derivative 158169
- 5. A Conditional Strong Dichotomy and Other Discussion 162173
- 6. Non-Singular Rank One Maps and Flat Polynomials 165176
- 7. Zeros of Polynomials 178189
- References 179190

- Diophantine approximation exponents on homogeneous varieties 181192
- Ergodicity of principal algebraic group actions 201212
- A note on three problems in metric Diophantine approximation 211222
- Dynamical invariants for group automorphisms 231242
- Back Cover Back Cover1272