Ergodic Theory: Advances in Dynamical Systems

by Idris Assani (Editor)

Overview

This monograph discusses recent advances in ergodic theory and dynamical systems. As a mixture of survey papers of active research areas and original research papers, this volume attracts young and senior researchers alike.

Contents:
Duality of the almost periodic and proximal relations
Limit directions of a vector cocycle, remarks and examples
Optimal norm approximation in ergodic theory
The iterated Prisoner’s Dilemma: good strategies and their dynamics
Lyapunov exponents for conservative twisting dynamics: a survey
Takens’ embedding theorem with a continuous observable

Product Details

ISBN-13:	9783110460865
Publisher:	De Gruyter
Publication date:	06/20/2016
Pages:	148
Product dimensions:	6.69(w) x 9.45(h) x (d)
Age Range:	18 Years

About the Author

Idris Assani, University of North Carolina at Chapel Hill, USA.

Table of Contents

Duality of the almost periodic and proximal relations Joseph Auslander Gernot Greschonig 1

1 Introduction 1

2 Almost periodic and proximal relations of a flow 2

3 Distal and proximal equivalence of minimal flows 6

4 Proximal and almost periodic cells of a flow 11

References 13

Limit directions of a vector cocycle, remarks and examples Jean-Pierre Conze Stéphane Le Borgne 14

Introduction 14

1 Preliminaries 15

2 Limit directions of a vector cocycle, general properties 17

3 Application of the CLT, martingales and invariance principle 30

References 38

Optimal norm approximation in ergodic theory Joseph Rosenblatt 40

1 Introduction 40

2 Basics 41

3 Discrete Spectrum Case 43

4 Weak Mixing Case 47

5 General Case 50

6 Properties of O^r_n 53

7 Oscillation and generic behavior for transformations 56

8 Cocycles 64

9 Other Lebesgue spaces 69

References 75

The iterated Prisoner's Dilemma: good strategies and their dynamics Ethan Akin 77

1 The iterated Prisoner's Dilemma 77

2 Good plans and the Press-Dyson decomposition 86

3 Competing zero-determinant strategies 94

4 Dynamics among zero-determinant strategies 97

References 107

Lyapunov exponents for conservative twisting dynamics: a survey Marie-Claude Arnaud 108

1 Twisting conservative dynamics 109

2 Lyapunov exponents for the minimizing measures and angle of the Oseledets splitting 115

3 Shape of the support of the minimizing measures and Lyapunov exponents 126

References 132

Takens' embedding theorem with a continuous observable Yonatan Gutman 134

1 Introduction 134

2 Preliminaries 137

3 Proof of the theorem 138

References 141

Authors 142