Ergodic Theory on Compact Spaces

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