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1998 | 157 | 2-3 | 99-119
Tytuł artykułu

A cut salad of cocycles

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We study the centraliser of locally compact group extensions of ergodic probability preserving transformations. New methods establishing ergodicity of group extensions are introduced, and new examples of squashable and non-coalescent group extensions are constructed.
Słowa kluczowe
Rocznik
Tom
157
Numer
2-3
Strony
99-119
Opis fizyczny
Daty
wydano
1998
otrzymano
1997-07-23
poprawiono
1998-03-03
Twórcy
autor
  • School of Mathematical Sciences, Tel Aviv University, 69978 Tel Aviv, Israel, aaro@math.tau.ac.il
  • Department of Mathematics and Computer Science, Nicholas Copernicus University, Chopina 12/18, 87-100 Toruń, Poland, mlem@mat.uni.torun.edu.pl
  • Département de Mathématiques, Sité Colbert, Université de Rouen, 76821 Mont-Saint-Aignan Cedex, France, Dalibor.Volny@univ-rouen.fr
Bibliografia
  • [A1] J. Aaronson, The asymptotic distributional behaviour of transformations preserving infinite measures, J. Anal. Math. 39 (1981), 203-234.
  • [A2] J. Aaronson, The intrinsic normalising constants of transformations preserving infinite measures, ibid. 49 (1987), 239-270.
  • [A-L-M-N] J. Aaronson, M. Lemańczyk, C. Mauduit and H. Nakada, Koksma's inequality and group extensions of Kronecker transformations, in: Algorithms, Fractals and Dynamics (Okayama and Kyoto, 1992), Y. Takahashi (ed.), Plenum, New York, 1995, 27-50.
  • [A-L-V] J. Aaronson, M. Lemańczyk and D. Volný, A salad of cocycles, preprint, internet: http://www.math.tau.ac.il/~aaro, 1995.
  • [D] A. Danilenko, Comparison of cocycles of measured equivalence relations and lifting problems, Ergodic Theory Dynam. Systems 18 (1998), 125-151.
  • [F-M] J. Feldman and C. C. Moore, Ergodic equivalence relations, cohomology, and von Neumann algebras, I, Trans. Amer. Math. Soc. 234 (1977), 289-324.
  • [G-L-S] P. Gabriel, M. Lemańczyk and K. Schmidt, Extensions of cocycles for hyperfinite actions and applications, Monatsh. Math. 123 (1997), 209-228.
  • [G-S] V. I. Golodets and S. D. Sinel'shchikov, Locally compact groups appearing as ranges of cocycles of ergodic ℤ-actions, Ergodic Theory Dynam. Systems 5 (1985), 45-57.
  • [H] P. Halmos, Lectures on Ergodic Theory, Chelsea, New York, 1953.
  • [H-P] F. Hahn and W. Parry, Some characteristic properties of dynamical systems with quasi-discrete spectrum, Math. Systems Theory 2 (1968), 179-190.
  • [H-O-O] T. Hamachi, Y. Oka and M. Osikawa, A classification of ergodic non-singular transformation groups, Mem. Fac. Sci. Kyushu Univ. Ser. A 28 (1974), 113-133.
  • [K-W] Y. Katznelson and B. Weiss, Commuting measure preserving transformations, Israel J. Math. 12 (1972), 161-172.
  • [K] W. Krieger, On ergodic flows and isomorphism of factors, Math. Ann. 223 (1976), 19-70.
  • [L-L-T] M. Lemańczyk, P. Liardet and J-P. Thouvenot, Coalescence of circle extensions of measure preserving transformations, Ergodic Theory Dynam. Systems 12 (1992), 769-789.
  • [L-V] P. Liardet and D. Volný, Sums of continuous and differentiable functions in dynamical systems, Israel J. Math. 98 (1997), 29-60.
  • [L] D. Lind, Locally compact measure preserving flows, Adv. Math. 15 (1975), 175-193.
  • [M] D. Maharam, Incompressible transformations, Fund. Math. 56 (1964), 35-50.
  • [M-S] C. Moore and K. Schmidt, Coboundaries and homomorphisms for non-singular actions and a problem of H. Helson, Proc. London Math. Soc. 40 (1980), 443-475.
  • [O] D. Ornstein, Ergodic Theory, Randomness, and Dynamical Systems, Yale Math. Monographs 5, Yale Univ. Press, New Haven, 1974.
  • [O-W] D. Ornstein and B. Weiss, Entropy and isomorphism theorems for actions of amenable groups, J. Anal. Math. 48 (1987), 1-142.
  • [R] D. Rudolph, Classifying the isometric extensions of a Bernoulli shift, ibid. 34 (1978), 36-60.
  • [S] K. Schmidt, Cocycles of Ergodic Transformation Groups, Lecture Notes in Math. 1, Mac Millan of India, 1977.
  • [Z] R. Zimmer, Amenable ergodic group actions and an application to Poisson boundaries of random walks, J. Funct. Anal. 27 (1978), 350-372.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-fmv157i2p99bwm
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