An Introduction to Ergodic Theory

Graduate Texts in Mathematics 79

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ISBN/EAN: 9780387951522
Sprache: Englisch
Umfang: IX, 250 S., 8 Fotos
Format (T/L/B): 1.5 x 23.5 x 15.5 cm
Auflage: 1. Auflage 1982
Einband: kartoniertes Buch


The first part of this introduction to ergodic theory addresses measure-preserving transformations of probability spaces and covers such topics as recurrence properties and the Birkhoff ergodic theorem. The second part focuses on the ergodic theory of continuous transformations of compact metrizable spaces. Several examples are detailed, and the final chapter outlines results and applications of ergodic theory to other branches of mathematics.


Preliminaries.- Measure-Preserving Transformations.- Isomorphism, Conjugacy, and Spectral Isomorphism.- Measure-Preserving Transformations with Discrete Spectrum.- Entropy.- Topological Dynamics.- Invariant Measures for Continuous Transformations.- Topological Entropy.- Relationship Between Topological Entropy and Mesaure-Theoretic Entropy.- Topological Pressure and Its Relationship with Invariant Measures.- Applications and Other Topics.

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