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2000 | 84/85 | 2 | 307-317
Tytuł artykułu

Residuality of dynamical morphisms

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We present a unified approach to the finite generator theorem of Krieger, the homomorphism theorem of Sinai and the isomorphism theorem of Ornstein. We show that in a suitable space of measures those measures which define isomorphisms or respectively homomorphisms form residual subsets.
Słowa kluczowe
Rocznik
Tom
Numer
2
Strony
307-317
Opis fizyczny
Daty
wydano
2000
otrzymano
1999-08-03
poprawiono
1999-12-01
Twórcy
autor
  • Department of Mathematics, Oregon State University, Corvallis, OR 97331-4665 U.S.A.
autor
  • Centre for Mathematics and Computer Science (CWI), Post Office Box 94079, 1090 GB Amsterdam, The Netherlands
  • Institute of Mathematics, Wrocław University of Technology, Wybrzeże Wyspiańskiego 27, 50-370 Wrocław, Poland
Bibliografia
  • [1] P. Billingsley, Ergodic Theory and Information, Wiley, New York, 1965.
  • [2] R. Burton and A. Rothstein, Isomorphism theorems in ergodic theory, Technical Report, Oregon State Univ., 1977.
  • [3] H. Furstenberg, Recurrence in Ergodic Theory and Combinatorial Number Theory, Princeton Univ. Press, Princeton, NJ, 1981.
  • [4] P. Halmos and H. Vaughan, The Marriage Problem, Amer. J. Math.72 (1950), 214-215.
  • [5] K. Jacobs, Lecture Notes on Ergodic Theory, Aarhus Univ., 1962.
  • [6] J. Kammeyer, The isomorphism theorem for relatively finitely determined $ℤ^n$-actions, Israel J. Math.69 (1990), 117-127.
  • [7] M. Keane and J. Serafin, On the countable generator theorem, Fund. Math.157 (1998), 255-259.
  • [8] M. Keane and M. Smorodinsky, Bernoulli schemes of the same entropy are finitarily isomorphic, Ann. of Math.109 (1979), 397-406.
  • [9] W. Krieger, On entropy and generators of measure-% preserving transformations, Trans. Amer. Math. Soc.149 (1970), 453-464.
  • [10] V. A. Rokhlin, Lectures on the entropy theory of measure-preserving transformations, Russian Math. Surveys22 (1967), no. 5, 1-52.
  • [11] D. Ornstein, Bernoulli shifts with the same entropy are isomorphic, Adv. Math.4 (1970), 337-352.
  • [12] D. Ornstein, Ergodic Theory, Randomness and Dynamical Systems, Yale Univ. Press, New Haven, 1974.
  • [13] J. Serafin, Finitary codes and isomorphisms, Ph.D. Thesis, Technische Universiteit Delft, 1996.
  • [14] Ya. Sinai, A weak isomorphism of transformations with an invariant measure, Dokl. Akad. Nauk SSSR 147 (1962), 797-800 (in Russian).
  • [15] P. Walters, An Introduction to Ergodic Theory, Springer, 1982.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-cmv84i2p307bwm
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