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Basic ergodic theory

Author: M G Nadkarni
Publisher: Basel ; Boston : Birkhauser Verlag, [1998]
Edition/Format:   Print book : English : 2nd edView all editions and formats
Summary:

Focuses on ergodic theory. Suitable for those with a background in basic measure theory and metric topology, this book covers the basic topics of ergodic theory such as the Poincare recurrence lemma,  Read more...

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Additional Physical Format: Online version:
Nadkarni, M.G. (Mahendra Ganpatrao), 1939-
Basic ergodic theory.
Basel ; Boston : Birkhauser Verlag, [1998]
(OCoLC)806179706
Material Type: Internet resource
Document Type: Book, Internet Resource
All Authors / Contributors: M G Nadkarni
ISBN: 3764358165 9783764358167 0817658165 9780817658168
OCLC Number: 39800545
Notes: "Birkhaüser advanced texts."
Description: vi, 149 pages : illustrations ; 24 cm
Contents: The Poincare recurrence lemma - standard Borel spaces, Borel automorphisms, orbit equivalence and isomorphism, poincare recurrence lemma, asides; ergodic theorems of Birkhoff and von Neumann - ergodic theorem for permutations, easy generalisations, almost periodic functions, Birkhoff's ergodic theorem, von Neumann ergodic theorem, ergodic theorems for return times, asides; ergodicity - discussion of ergodicity, irrational rotation, diadic adding machine; mixing conditions and their characterisations; Bernoulli shift and related concepts - Bernoulli shifts, Kolmogorov consistency theorem, Markov shift, Kolmogorov shifts and related concepts, non-invertible shifts, diadic adding machine, Hewitt-Savage Zero-one law; discrete spectrum theorem - spectral isomorphism of Brenoulli shifts, entropy; induced automorphisms and related concepts - Kakutani towers, periodic approximations, Rokhlin's lemma, induced automorphisms, automorphism built under a function, Kakutani equivalence, rank of an automorphism, countable generators, rank of an automorphism; Borel automorphisms are polish homeomorphisms; the Glimm-Effros theorem; E. Hopf's theorem -compressibility (in the sense of Brikhoff and Smith), compressibility (in the sense of Hopf), compressibility, ergodic theorem (measure free proof), ergodic decomposition, proof of Hopf's theorem, orbit equivalence, generalisations and counter-examples; H. Dye's theorem; flows and their representations - definitions and examples, flow built under a function, topology for a flow, existence of countable cross-sections, representation of non-singular flows, representation of measure preserving flows.
Responsibility: M.G. Nadkarni.

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"This relatively short book is, for anyone new to ergodic theory, admirably broad in scope. The exposition is clear, and the brevity of the book has not been achieved by giving terse proofs. The Read more...

 
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