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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$89.95$
V. I. Arnol′d and A. Avez, Ergodic problems of classical mechanics, W. A. Benjamin, Inc., New York-Amsterdam, 1968. Translated from the French by A. Avez. MR 0232910
Roy L. Adler and Benjamin Weiss, Similarity of automorphisms of the torus, Memoirs of the American Mathematical Society, No. 98, American Mathematical Society, Providence, R.I., 1970. MR 0257315
[Ber67] K. Berg, On the conjugacy problem for k-systems, Ph.D Thesis, University of Minnesota (1967).
Rufus Bowen, Markov partitions for Axiom $\textrm {A}$ diffeomorphisms, Amer. J. Math. 92 (1970), 725–747. MR 277003, DOI 10.2307/2373370
Paul R. Halmos, On automorphisms of compact groups, Bull. Amer. Math. Soc. 49 (1943), 619–624. MR 8647, DOI 10.1090/S0002-9904-1943-07995-5
Paul R. Halmos, Lectures on ergodic theory, Publications of the Mathematical Society of Japan, vol. 3, Mathematical Society of Japan, Tokyo, 1956. MR 0097489
[Jew70] R. Jewitt, The prevelance of uniquely ergodic systems, Journal of Mathematical Mechanics 19 (1970), 717-729.
Yitzhak Katznelson, Ergodic automorphisms of $T^{n}$ are Bernoulli shifts, Israel J. Math. 10 (1971), 186–195. MR 294602, DOI 10.1007/BF02771569
A. N. Kolmogorov, A new metric invariant of transient dynamical systems and automorphisms in Lebesgue spaces, Dokl. Akad. Nauk SSSR (N.S.) 119 (1958), 861–864 (Russian). MR 0103254
A. N. Kolmogorov, A new metric invariant of transient dynamical systems and automorphisms in Lebesgue spaces, Dokl. Akad. Nauk SSSR (N.S.) 119 (1958), 861–864 (Russian). MR 0103254
Wolfgang Krieger, On entropy and generators of measure-preserving transformations, Trans. Amer. Math. Soc. 149 (1970), 453–464. MR 259068, DOI 10.1090/S0002-9947-1970-0259068-3
Wolfgang Krieger, On unique ergodicity, Proceedings of the Sixth Berkeley Symposium on Mathematical Statistics and Probability (Univ. California, Berkeley, Calif., 1970/1971) Univ. California Press, Berkeley, Calif., 1972, pp. 327–346. MR 0393402
Donald Ornstein, Bernoulli shifts with the same entropy are isomorphic, Advances in Math. 4 (1970), 337–352. MR 257322, DOI 10.1016/0001-8708(70)90029-0
William Parry, Intrinsic Markov chains, Trans. Amer. Math. Soc. 112 (1964), 55–66. MR 161372, DOI 10.1090/S0002-9947-1964-0161372-1
C. E. Shannon, A mathematical theory of communication, Bell System Tech. J. 27 (1948), 379–423, 623–656. MR 26286, DOI 10.1002/j.1538-7305.1948.tb01338.x
Ja. Sinaĭ, On the concept of entropy for a dynamic system, Dokl. Akad. Nauk SSSR 124 (1959), 768–771 (Russian). MR 0103256
[Sin59b] -, The notion of entropy of a dynamical system, Academiia Nauk SSSR, Doklady 125 (1959), 768-771.
Ja. G. Sinaĭ, Construction of Markov partitionings, Funkcional. Anal. i Priložen. 2 (1968), no. 3, 70–80 (Loose errata) (Russian). MR 0250352
- [AA68]
- V.I. Arnold and A. Avez, Ergodic problems of classical mechanics, Benjamin, 1968. MR 0232910
- [AW70]
- R. Adler and B. Weiss, Similarity of automorphisms of the torus, Memoirs of the American Mathematical Society 98 (1970). MR 0257315
- [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
- [Hal43]
- P.R. Halmos, On automorphisms of compact groups, Bulletin of the American Mathematical Society 49 (1943), 619-624. MR 0008647
- [Hal56]
- -, Ergodic theory, The Mathematical Society of Japan, 1956. MR 0097489
- [Jew70]
- R. Jewitt, The prevelance of uniquely ergodic systems, Journal of Mathematical Mechanics 19 (1970), 717-729.
- [Kat71]
- Y. Katznelson, Ergodic automorphisms of
are Bernoulli shifts, Israel Journal of Mathematics 10 (1971), 186-195. MR 0294602
- [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
- [Kol59]
- -, Entropy per unit time as a metric invariant of automorphisms, Academiia Nauk SSSR, Doklady 124 (1959), 754-755. MR 0103254
- [Kri70]
- W. Krieger, On entropy and generators of measure-preserving transformations, Transactions of the American Mathematical Society 149 (1970), 453-464. MR 0259068
- [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
- [Orn70]
- D.S. Ornstein, Bernoulli shifts with the same entropy are isomorphic, Advances in Mathematics 4 (1970), 337-352. MR 0257322
- [Par64]
- W. Parry, Intrinsic Markov chains, Transactions of the American Mathematical Society 112 (1964), 55-66. MR 0161372
- [Sha48]
- C. Shannon, A mathematical theory of communication, Bell Systems Technical Journal 27 (1948), 379-473, 623-656. MR 0026286
- [Sin59a]
- Y.G. Sinai, Flows with finite entropy, Academiia Nauk SSSR, Doklady 125 (1959), 1200-1202. MR 0103256
- [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
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
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.
