Slow entropy type invariants and smooth realization of commuting measure-preserving transformations

Anatole Katok; Jean-Paul Thouvenot

Annales de l'I.H.P. Probabilités et statistiques (1997)

  • Volume: 33, Issue: 3, page 323-338
  • ISSN: 0246-0203

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Katok, Anatole, and Thouvenot, Jean-Paul. "Slow entropy type invariants and smooth realization of commuting measure-preserving transformations." Annales de l'I.H.P. Probabilités et statistiques 33.3 (1997): 323-338. <http://eudml.org/doc/77571>.

@article{Katok1997,
author = {Katok, Anatole, Thouvenot, Jean-Paul},
journal = {Annales de l'I.H.P. Probabilités et statistiques},
keywords = {measure-preserving actions; exponential growth rate; invariant measure},
language = {eng},
number = {3},
pages = {323-338},
publisher = {Gauthier-Villars},
title = {Slow entropy type invariants and smooth realization of commuting measure-preserving transformations},
url = {http://eudml.org/doc/77571},
volume = {33},
year = {1997},
}

TY - JOUR
AU - Katok, Anatole
AU - Thouvenot, Jean-Paul
TI - Slow entropy type invariants and smooth realization of commuting measure-preserving transformations
JO - Annales de l'I.H.P. Probabilités et statistiques
PY - 1997
PB - Gauthier-Villars
VL - 33
IS - 3
SP - 323
EP - 338
LA - eng
KW - measure-preserving actions; exponential growth rate; invariant measure
UR - http://eudml.org/doc/77571
ER -

References

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  1. [1] A. Katok, Monotone equivalence in ergodic theory, Math. USSR, Izvestija, Vol. 11, 1977, pp. 99-146. Zbl0379.28008MR442195
  2. [2] A. Katok, Lyapunov exponents, entropy and periodic orbits for diffeomorphisms, Publ. Math IHES, Vol 51, 1980, pp. 137-173. Zbl0445.58015MR573822
  3. [3] A. Katok, Constructions in ergodic theory, preprint. Zbl1030.37001
  4. [4] A. Kakot and B. Hasselblatt, Introduction to the modern theory of dynamical systems, Cambridge University Press, New York, 1995. Zbl0878.58020MR1326374
  5. [5] S. Katok, An estimate from above for the topological entropy of a diffeomorphism, Global theory of Dynamical systems, Lecture Note Math., Vol. 819, Springer Verlag, 1980, pp. 258-266. Zbl0448.58010MR591188
  6. [6] A.G. Kushnirenko, An upper bound of the entropy of classical dynamical systems, Sov. Math. Dokl., Vol. 6, 1965, pp. 360-362. Zbl0136.42905
  7. [7] D. Lind and J.-P. Thouvenot, Measure-preserving homeomorphisms of the torus represent all finite entropy ergodic transformations, Math. Systems Theory, Vol. 11, 1977, pp. 275-285. Zbl0377.28011MR584588
  8. [8] D. Ornstein and B. Weiss, Isomorphism theorem for amenable group actions, J. Anal. Math., Vol. 48, 1987, p. 1-141. Zbl0637.28015MR910005
  9. [9] Ya.B. Pesin, Characteristic Lyapunov exponents and smooth ergodic theory, Russian Math. Surveys, Vol. 32, 1977, pp. 55-114. Zbl0383.58011MR466791
  10. [10] D. Ruelle, An inequality for the entropy of differentiable maps, Bol. Soc. Brasil. Math., Vol. 9, 1978, pp. 83-87. Zbl0432.58013MR516310

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