Topics in Dynamics and Ergodic Theory

This book contains a collection of survey papers by leading researchers in ergodic theory, low-dimensional and topological dynamics.

Sergey Bezuglyi (Edited by), Sergiy Kolyada (Edited by)

9780521533652, Cambridge University Press

Paperback, published 8 December 2003

270 pages, 23 b/w illus. 4 tables 20 exercises
22.8 x 15.2 x 1.7 cm, 0.375 kg

This book contains a collection of survey papers by leading researchers in ergodic theory, low-dimensional and topological dynamics and it comprises nine chapters on a range of important topics. These include: the role and usefulness of ultrafilters in ergodic theory, topological dynamics and Ramsey theory; topological aspects of kneading theory together with an analogous 2-dimensional theory called pruning; the dynamics of Markov odometers, Bratteli-Vershik diagrams and orbit equivalence of non-singular automorphisms; geometric proofs of Mather's connecting and accelerating theorems; recent results in one dimensional smooth dynamics; periodic points of nonexpansive maps; arithmetic dynamics; the defect of factor maps; entropy theory for actions of countable amenable groups.

1. Introductory talk at the opening of the conference Anatole M. Stepin
2. Minimal idempotents and ergodic Ramsey theory Vitaly Bergelson
3. Symbolic dynamics and topological models in dimensions 1 and 2 André de Carvalho and Toby Hall
4. Markov odometers Anthony H. Dooley
5. Geometric proofs of Mather's connecting and accelerating theorems Vadim Kaloshin
6. Structural stability in one dimensional dynamics Oleg Kozlovski
7. Periodic points of nonexpansive maps: a survey Bas Lemmens
8. Arithmetic dynamics Nikita Sidorov
9. The defect of factor maps and finite equivalence of dynamical systems Klaus Thomsen
10. Actions of amenable groups Benjamin Weiss.

Subject Areas: Nonlinear science [PBWR], Calculus & mathematical analysis [PBK]