Ergodic Theory on Compact Spaces

摘要: Measure-theoretic dynamical systems.- Measures on compact metric spaces.- Invariant measures for continuous tranformations.- Time averages.- Ergodicity.- Mixing and transitivity.- Shifts subshifts.- the shift space.- Partitions generators.- Information entropy.- The computation of Entropy Bernoulli Markov shifts.- Ergodic decompositions.- Topological Expansive homeomorphisms.- Subshifts finite type.- variational principle topological with maximal entropy-Intrinsically ergodic Entropy-Expansive specification property.- Specification expansiveness.- Basic sets axiom A.- Automorphisms torus.- More subshifts Preparations generator theorems.- Combinatorial construction minimal sets.- Finite generators transformations (theorem Krieger).- Strictly embedding (Theorem Jewett aperiodic transformations.- Embedding theorems transformations.