A cut salad of cocycles
Aaronson, Jon ; Lemańczyk, Mariusz ; Volný, Dalibor
Fundamenta Mathematicae, Tome 158 (1998), p. 99-119 / Harvested from The Polish Digital Mathematics Library

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.

Publié le : 1998-01-01
EUDML-ID : urn:eudml:doc:212297
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     title = {A cut salad of cocycles},
     journal = {Fundamenta Mathematicae},
     volume = {158},
     year = {1998},
     pages = {99-119},
     zbl = {0966.28010},
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Aaronson, Jon; Lemańczyk, Mariusz; Volný, Dalibor. A cut salad of cocycles. Fundamenta Mathematicae, Tome 158 (1998) pp. 99-119. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-fmv157i2p99bwm/

[00000] [A1] J. Aaronson, The asymptotic distributional behaviour of transformations preserving infinite measures, J. Anal. Math. 39 (1981), 203-234. | Zbl 0499.28013

[00001] [A2] J. Aaronson, The intrinsic normalising constants of transformations preserving infinite measures, ibid. 49 (1987), 239-270. | Zbl 0644.28013

[00002] [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. | Zbl 0878.28009

[00003] [A-L-V] J. Aaronson, M. Lemańczyk and D. Volný, A salad of cocycles, preprint, internet: http://www.math.tau.ac.il/~aaro, 1995.

[00004] [D] A. Danilenko, Comparison of cocycles of measured equivalence relations and lifting problems, Ergodic Theory Dynam. Systems 18 (1998), 125-151. | Zbl 0919.28015

[00005] [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.

[00006] [G-L-S] P. Gabriel, M. Lemańczyk and K. Schmidt, Extensions of cocycles for hyperfinite actions and applications, Monatsh. Math. 123 (1997), 209-228. | Zbl 0887.28008

[00007] [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.

[00008] [H] P. Halmos, Lectures on Ergodic Theory, Chelsea, New York, 1953.

[00009] [H-P] F. Hahn and W. Parry, Some characteristic properties of dynamical systems with quasi-discrete spectrum, Math. Systems Theory 2 (1968), 179-190. | Zbl 0167.32902

[00010] [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. | Zbl 0293.28011

[00011] [K-W] Y. Katznelson and B. Weiss, Commuting measure preserving transformations, Israel J. Math. 12 (1972), 161-172. | Zbl 0239.28014

[00012] [K] W. Krieger, On ergodic flows and isomorphism of factors, Math. Ann. 223 (1976), 19-70. | Zbl 0332.46045

[00013] [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. | Zbl 0785.58030

[00014] [L-V] P. Liardet and D. Volný, Sums of continuous and differentiable functions in dynamical systems, Israel J. Math. 98 (1997), 29-60. | Zbl 0881.28012

[00015] [L] D. Lind, Locally compact measure preserving flows, Adv. Math. 15 (1975), 175-193. | Zbl 0293.28012

[00016] [M] D. Maharam, Incompressible transformations, Fund. Math. 56 (1964), 35-50. | Zbl 0133.00304

[00017] [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. | Zbl 0428.28014

[00018] [O] D. Ornstein, Ergodic Theory, Randomness, and Dynamical Systems, Yale Math. Monographs 5, Yale Univ. Press, New Haven, 1974.

[00019] [O-W] D. Ornstein and B. Weiss, Entropy and isomorphism theorems for actions of amenable groups, J. Anal. Math. 48 (1987), 1-142.

[00020] [R] D. Rudolph, Classifying the isometric extensions of a Bernoulli shift, ibid. 34 (1978), 36-60. | Zbl 0415.28012

[00021] [S] K. Schmidt, Cocycles of Ergodic Transformation Groups, Lecture Notes in Math. 1, Mac Millan of India, 1977. | Zbl 0421.28017

[00022] [Z] R. Zimmer, Amenable ergodic group actions and an application to Poisson boundaries of random walks, J. Funct. Anal. 27 (1978), 350-372. | Zbl 0391.28011