Ergodic Theory on Compact Spaces

von M. Denker, C. Grillenberger, K. Sigmund

368 Seiten, Taschenbuch

Kurzbeschreibung des Verlags

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

• Reihe: Lecture Notes in Mathematics
• Themen: Mathematik und Naturwissenschaften Mathematik
• ISBN: 9783540077978
• Sprache: Englisch
• Erscheinungsdatum: 01.07.1976
• Größe: 235 x 155 mm
• Verlag: Springer