On extremal and perfect σ-algebras for flows

• Autorzy: B. Kamiński , Z. S. Kowalski
• Języki publikacji: EN

Abstrakty

EN

It is shown that there exists a flow on a Lebesgue space with finite entropy and an extremal σ-algebra of it which is not perfect.

Kategorie tematyczne

• 28D10: One-parameter continuous families of measure-preserving transformations

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 1998
• Tom: 129
• Numer: 2
• Strony: 179-183

Daty

wydano

1998

otrzymano

1997-05-06

poprawiono

1997-11-03

Twórcy

autor

B. Kamiński

• Faculty of Mathematics and Informatics, Institute of Mathematics, Nicholas Copernicus University, Chopina 12/18, Toruń, Polanf

autor

Z. S. Kowalski

• Wrocław Technical University, Wybrzeże Wyspiańskiego 27, 87-100 Toruń, Poland 50-370 Wrocław, Poland

Bibliografia

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• [2] F. Blanchard, K-flots et théorème de renouvellement, ibid., 345-358.
• [3] M. Binkowska and B. Kamiński, Entropy increase for $ℤ^d$-actions on a Lebesgue space, Israel J. Math. 88 (1994), 307-318.
• [4] S. Goldstein and O. Penrose, A non-equilibrium entropy for dynamical systems, J. Statist. Phys. 24 (1981), 325-343.
• [5] B. M. Gurevich, Some existence conditions for K-decompositions for special flows, Trans. Moscow Math. Soc. 17 (1967), 99-126.
• [6] B. M. Gurevich, Perfect partitions for ergodic flows, Funktsional. Anal. i Prilozhen. 11 (3) (1977), 20-23 (in Russian).
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• [8] B. Kamiński, Z. S. Kowalski and P. Liardet, On extremal and perfect σ-algebras for $ℤ^d$-actions, Studia Math. 124 (1997), 173-178.
• [9] V. A. Rokhlin, Lectures on the entropy theory of measure-preserving transformations, Uspekhi Mat. Nauk 22 (5) (1967), 3-56 (in Russian).
• [10] T. Shimano, An invariant of systems in the ergodic theory, Tôhoku Math. J. 30 (1978), 337-350.
• [11] T. Shimano, Multiplicity of helices of a special flow, ibid. 31 (1979), 49-55.
• [12] T. Shimano, Multiplicity of helices for a regularly increasing sequence of σ-fields, ibid. 36 (1984), 141-148.
• [13] T. Shimano, On helices for Kolmogorov system with two indices, Math. J. Toyama Univ. 14 (1991), 213-226.