**Contemporary Mathematics**

Volume: 215;
1998;
334 pp;
Softcover

MSC: Primary 54; 28; 34;

Print ISBN: 978-0-8218-0608-1

Product Code: CONM/215

List Price: $89.00

Individual Member Price: $71.20

**Electronic ISBN: 978-0-8218-7807-1
Product Code: CONM/215.E**

List Price: $89.00

Individual Member Price: $71.20

# Topological Dynamics and Applications

Share this page *Edited by *
*M. G. Nerurkar; D. P. Dokken; D. B. Ellis*

This book is a very readable exposition of the modern theory of topological dynamics and presents diverse applications to such areas as ergodic theory, combinatorial number theory and differential equations. There are three parts: 1) The abstract theory of topological dynamics is discussed, including a comprehensive survey by Furstenberg and Glasner on the work and influence of R. Ellis. Presented in book form for the first time are new topics in the theory of dynamical systems, such as weak almost-periodicity, hidden eigenvalues, a natural family of factors and topological analogues of ergodic decomposition. 2) The power of abstract techniques is demonstrated by giving a very wide range of applications to areas of ergodic theory, combinatorial number theory, random walks on groups and others. 3) Applications to non-autonomous linear differential equations are shown. Exposition on recent results about Floquet theory, bifurcation theory and Lyapanov exponents is given.

#### Table of Contents

# Table of Contents

## Topological Dynamics and Applications

- Contents vii8 free
- Preface ix10 free
- Part I. Topological Dynamics: Abstract Theory 112 free
- Robert Ellis and the algebra of dynamical systems 314
- Weak mixing and pure weak mixing minimal flows 1324
- A natural family of factors for minimal flows 1930
- Topological ergodic decomposition and homogeneous flows 4354
- On the proximal and regionally proximal relation of an extension between minimal flows 5364
- Almost equicontinuity and the enveloping semigroup 7586
- Some universal constructions in abstract topological dynamics 8394
- Weakly almost periodic flows and hidden eigenvalues 101112
- Enveloping linear maps 121132
- An overview of the construction of suspension flows using continuous cocycles 133144
- Suspensions, inheritance, and flows on homogeneous spaces 149160
- On the lifting of transformation semigroups 159170

- Part II. Applications and Other Dynamical Results 167178
- Idempotent measures associated to a locally compact topological group 169180
- Another proof of Moore's ergodicity theorem for SL(2, R) 183194
- Multiple recurrence and doubly minimal systems 189200
- Subset dynamics and van der Waerden's theorem 197208
- Recurrence for semigroup actions and a non-commutative Schur theorem 205216
- A note on Livšic's periodic point theorem 223234
- A zero-one law for dynamical properties 231242
- Residuality and orbit equivalence 243254
- Uncountably many Vershik-inequivalent group actions of equal entropy 255266

- Part III. Applications to Differential Equations 263274
- Positive exponents for a dense set of continuous SL(2, R) valued cocycles which arise as solutions to strongly accessible linear differential systems 265276
- Topological dynamics and differential equations 279290
- An ergodic and topological approach to almost periodic bidimensional linear systems 299310
- An application of topological dynamics to bifurcation theory 323334

#### Readership

Graduate students and research mathematicians working in ergodic theory, topological dynamics, differential equations and dynamical systems.