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Bulletin of the American Mathematical Society
ISSN 1088-9485(e) ISSN 0273-0979(p)

     

Book Review

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Book Information

Author(s): Geon Ho Choe
Title: Computational ergodic theory
Additional book information: Springer, Berlin, Heidelberg, New York, 2005, 472 pp., US$89.95, ISBN 3-540-23121-8

References:

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K. Berg, On the conjugacy problem for k-systems, Ph.D Thesis, University of Minnesota (1967).

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P.R. Halmos, On automorphisms of compact groups, Bulletin of the American Mathematical Society 49 (1943), 619-624. MR 0008647 (5:40c)

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-, Ergodic theory, The Mathematical Society of Japan, 1956. MR 0097489 (20:3958)

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R. Jewitt, The prevelance of uniquely ergodic systems, Journal of Mathematical Mechanics 19 (1970), 717-729.

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Y. Katznelson, Ergodic automorphisms of $ \mathbb{T}^n$ are Bernoulli shifts, Israel Journal of Mathematics 10 (1971), 186-195. MR 0294602 (45:3672)

[Kol58]
A. Kolmogorov, A new metric invariant for transient dynamical systems and automorphisms in Lebesgue spaces, Academiia Nauk SSSR, Doklady 119 (1958), 861-864. MR 0103254 (21:2035a)

[Kol59]
-, Entropy per unit time as a metric invariant of automorphisms, Academiia Nauk SSSR, Doklady 124 (1959), 754-755. MR 0103255 (21:2035b)

[Kri70]
W. Krieger, On entropy and generators of measure-preserving transformations, Transactions of the American Mathematical Society 149 (1970), 453-464. MR 0259068 (41:3710)

[Kri72]
-, On unique ergodicity, Proceedings of the Sixth Berkeley Symposium on Mathematical Statistics and Probability, Volume II, Probability Theory, University of California Press, 1972, pp. 327-346. MR 0393402 (52:14212)

[Orn70]
D.S. Ornstein, Bernoulli shifts with the same entropy are isomorphic, Advances in Mathematics 4 (1970), 337-352. MR 0257322 (41:1973)

[Par64]
W. Parry, Intrinsic Markov chains, Transactions of the American Mathematical Society 112 (1964), 55-66. MR 0161372 (28:4579)

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C. Shannon, A mathematical theory of communication, Bell Systems Technical Journal 27 (1948), 379-473, 623-656. MR 0026286 (10:133e)

[Sin59a]
Y.G. Sinai, Flows with finite entropy, Academiia Nauk SSSR, Doklady 125 (1959), 1200-1202. MR 0103257 (21:2036b)

[Sin59b]
-, The notion of entropy of a dynamical system, Academiia Nauk SSSR, Doklady 125 (1959), 768-771.

[Sin68]
-, Construction of Markov partitionings, Funkcional'nyi Analiz i Ego Prilozheniya zen 2 (1968), 245-253. MR 0250352 (40:3591)

Additional Information:

Reviewer(s):
Bruce Kitchens
Affiliation: Indiana U. Purdue U. Indianapolis
Email: bkitchens@math.iupui.edu

Review Information:
Journal: Bull. Amer. Math. Soc. 44 (2007), 147-155.

MSC (2000): Primary 37Axx
PII: S 0273-0979(06)01120-7
Posted: October 2, 2006
Copyright of article: Copyright 2006, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.




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