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Book Review

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Book Information:

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

References [Enhancements On Off] (What's this?)

  • [AA68] V.I. Arnold and A. Avez, Ergodic problems of classical mechanics, Benjamin, 1968. MR 0232910 (38:1233)
  • [AW70] R. Adler and B. Weiss, Similarity of automorphisms of the torus, Memoirs of the American Mathematical Society 98 (1970). MR 0257315 (41:1966)
  • [Ber67] K. Berg, On the conjugacy problem for k-systems, Ph.D Thesis, University of Minnesota (1967).
  • [Bow70] R. Bowen, Markov partitions for axiom A diffeomorphisms, American Journal of Mathematics 92 (1970), 725-747. MR 0277003 (43:2740)
  • [Hal43] P.R. Halmos, On automorphisms of compact groups, Bulletin of the American Mathematical Society 49 (1943), 619-624. MR 0008647 (5:40c)
  • [Hal56] -, Ergodic theory, The Mathematical Society of Japan, 1956. MR 0097489 (20:3958)
  • [Jew70] R. Jewitt, The prevelance of uniquely ergodic systems, Journal of Mathematical Mechanics 19 (1970), 717-729.
  • [Kat71] 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)
  • [Sha48] 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)

Review Information:

Reviewer: Bruce Kitchens
Affiliation: Indiana U. Purdue U. Indianapolis
Email: bkitchens@math.iupui.edu
Journal: Bull. Amer. Math. Soc. 44 (2007), 147-155
MSC (2000): Primary 37Axx
Published electronically: October 2, 2006
Review copyright: © Copyright 2006 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.
American Mathematical Society