Ergodic Theory on Compact Spaces

Manfred Denker, Christian Grillenberger, Karl Sigmund (auth.)9780387077970, 0-387-07797-9

Table of contents :
Introduction….Pages 1-2
Measure-theoretic dynamical systems….Pages 3-7
Measures on compact metric spaces….Pages 8-16
Invariant measures for continuous tranformations….Pages 17-19
Time averages….Pages 20-22
Ergodicity….Pages 23-29
Mixing and transitivity….Pages 30-35
Shifts and subshifts….Pages 36-40
Measures on the shift space….Pages 41-48
Partitions and generators….Pages 49-55
Information and entropy….Pages 56-61
The computation of entropy….Pages 62-67
Entropy for Bernoulli and Markov shifts….Pages 68-72
Ergodic decompositions….Pages 73-81
Topological entropy….Pages 82-91
Topological generators….Pages 92-102
Expansive homeomorphisms….Pages 103-116
Subshifts of finite type….Pages 117-130
The variational principle for topological entropy….Pages 131-146
Measures with maximal entropy—Intrinsically ergodic systems….Pages 147-159
Entropy—Expansive homeomorphisms….Pages 160-192
The specification property….Pages 193-209
Specification and expansiveness….Pages 210-223
Basic sets for axiom A….Pages 224-233
Automorphisms of the torus….Pages 234-240
More on subshifts of finite type….Pages 241-253
Preparations for generator theorems….Pages 254-274
Combinatorial construction of minimal sets….Pages 275-280
Finite generators for ergodic transformations (theorem of Krieger)….Pages 281-299
Strictly ergodic embedding (Theorem of Jewett and Krieger)….Pages 300-308
Finite generators for aperiodic transformations….Pages 309-315
Embedding theorems for aperiodic transformations….Pages 316-332