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This comprehensive text on entropy covers three major types of dynamics:
measure-preserving transformations; continuous maps on compact spaces; and
operators on function spaces.
Part I contains proofs of the Shannon–McMillan–Breiman Theorem, the
Ornstein–Weiss Return Time Theorem, the Krieger Generator Theorem, the Sinai and
Ornstein Theorems, and among the newest developments, the Ergodic Law of Series.
In Part II, after an expanded exposition of classical topological entropy, the book
addresses Symbolic Extension Entropy. It offers deep insight into the theory of entropy
structure and explains the role of zero-dimensional dynamics as a bridge between
measurable and topological dynamics. Part III explains how both measure-theoretic
and topological entropy can be extended to operators on relevant function spaces.
Intuitive explanations, examples, exercises and open problems make this an ideal
text for a graduate course on entropy theory. More experienced researchers can also
find inspiration for further research.
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