Abstract
We consider methods of establishing ergodicity of group extensions, proving that a class of cylinder flows are ergodic, coalescent and non-squashable. A new Koksma-type inequality is also obtained.
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References
J. Aaronson, The asymptotic distributional behaviour of transformations preserving infinite measures, J. d’Analyse Math., 39, (1981), 203–234.
The intrinsic normalising constants of transformations preserving infinite measures, J. d’Analyse Math., 49, (1987), 239–270.
L. Bagget, K. Merrill Smooth cocycles for an irrational rotation, preprint.
L. Bagget, K. Merrill, On the cohomological equation of a class of functions under irrational rotation of bounded type, preprint.
J.P.Conze, Ergodicite d’un flot cylindrique, Bull. Soc. Mat. de France, 108, (1980), 441–456.
H.Furstenberg, Strict ergodicity and transformations of the torus, Amer. J. Math., 83, (1961), 573–601.
M. Herman, Sur la conjugaison différentiable des difféomorphismes du cercle á des rotations, Publ. Mat. IHES, 49, (1979), 5–234.
P.Hellekalek, G.Larcher, On ergodicity of a class of skew products, Israel J. Math., 54, (1986), 301–306.
P.Hellekalek, G.Larcher, On Weyl sums and skew products over irrational rotations, Th. Comp. Sc., Fund. St., 65, (1989), 189–196.
A.B. Katok, Constructions in Ergodic Theory, preprint.
Y. Katznelson, An Introduction to Harmonic Analysis, Dover Publ. INC., New York (1967).
A. Krygin, Examples of ergodic cascades, Math. Notes USSR, 16, (1974), 1180–1186.
J. Kwiatkowski, M. Lemańczyk, D. Rudolph, Weak isomorphisms of measure-preserving diffeomorphisms, Israel J. Math. (1992), 33–64
J. Kwiatkowski, M. Lemańczyk, D. Rudolph, A class of real cocycles having an analytic coboundary modification, preprint.
L.Kuipers, H.Niederreiter, Uniform Distribution of Sequences, Wiley,(1974).
M. Lemanczyk, Ch. Mauduit, Ergodicity of a class of cocycles over irrational rotations, Bull. London Math. Soc., to appear.
I. Oren, Erdodicity of cylinder flows arising from irregularities of distribution, Israel J. Math., 44, (1983), 127–138.
D.A. Pask, Skew products over the irrational rotation, Israel J. Math., 69, (1990), 65–74.
D.A. Pask, Ergodicity of certain cylinder flows, Israel J. Math., 76, (1991) 129–152.
K. Schmidt Cocycles of Ergodic Transformation Groups, Lect. Notes in Math. Vol. 1, Mac Millan Co of India (1977).
R. Zimmer, Amenable ergodic group actions and an application to Poisson boundaries of random walks, J.Funct. Anal., 27, (1978), 350–372.
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© 1995 Plenum Press, New York
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Aaronson, J., Lemańczyk, M., Mauduit, C., Nakada, H. (1995). Koksma’s Inequality and Group Extensions of Kronecker Transformations. In: Takahashi, Y. (eds) Algorithms, Fractals, and Dynamics. Springer, Boston, MA. https://doi.org/10.1007/978-1-4613-0321-3_2
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DOI: https://doi.org/10.1007/978-1-4613-0321-3_2
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