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2000 | 84/85 | 1 | 29-41
Tytuł artykułu

Sur l'absence de mélange pour des flots spéciaux au-dessus d'une rotation irrationnelle

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Abstrakty
EN
We prove the absence of mixing for special flows built over (1) an irrational rotation and under a function whose Fourier coefficients are of order O(1/|n|), and (2) an irrational rotation (satisfying a diophantine condition) and under a function having a finite number of singularities of a logarithmic type. These results generalize two theorems of Kochergin.
Słowa kluczowe
Rocznik
Tom
Numer
1
Strony
29-41
Opis fizyczny
Daty
wydano
2000
otrzymano
1999-04-12
poprawiono
1999-12-15
Twórcy
  • Département de Mathématiques et d'Informatique, Université Nicolas Copernic, 12/18 rue Chopin, 87-100 Toruń, Pologne
Bibliografia
  • [1] J. Aaronson, An Introduction to Infinite Ergodic Theory, Math. Surveys Monogr. 50, Amer. Math. Soc., Providence, 1997.
  • [2] J. Aaronson, M. Lemańczyk, C. Mauduit and H. Nakada, Koksma's inequality and group extensions of Kronecker transformations, in: Algorithms, Fractals and Dynamics, Y. Takahashi (ed.), Plenum Press, 1995, 27-50.
  • [3] I. P. Cornfeld, S. V. Fomin and Ya. G. Sinai, Ergodic Theory, Springer, New York, 1982.
  • [4] G. H. Hardy and E. M. Wright, An Introduction to the Theory of Numbers, Clarendon, Oxford, 1960.
  • [5] K. M. Khanin and Ya. G. Sinai, Mixing of some classes of special flows over a circle rotation, Funktsional. Anal. i Prilozhen. 26 (1992), no. 3, 1-21 (in Russian).
  • [6] A. Ya. Khintchin, Continued Fractions, Univ. of Chicago Press, 1960.
  • [7] A. V. Kočergin [A. V. Kochergin], On the absence of mixing in special flows over the rotation of a circle and in flows on a two-dimensional torus, Dokl. Akad. Nauk SSSR 205 (1972), 515-518 (in Russian); English transl.: Soviet Math. Dokl. 13 (1972), 949-952.
  • [8] A. V. Kočergin [A. V. Kochergin], Time change for flows and mixing, Izv. Akad. Nauk SSSR Ser. Mat. 37 (1973), 1275-1298 (in Russian).
  • [9] A. V. Kočergin [A. V. Kochergin], On the mixing of special flows over interval exchange maps and in smooth flows on surfaces, Mat. Sb. 96 (1975), 471-502 (in Russian).
  • [10] A. V. Kočergin [A. V. Kochergin], Nonsingular saddle points and the absence of mixing, Mat. Zametki 19 (1976), 453-468 (in Russian); English transl.: Math. Notes 19 (1976), 277-286.
  • [11] L. Kuipers and H. Niederreiter, Uniform Distribution of Sequences, Wiley, 1974.
  • [12] M. Lemańczyk and C. Mauduit, Ergodicity of a class of cocycles over irrational rotations, J. London Math. Soc. 49 (1994), 124-132.
  • [13] M. Lemańczyk, F. Parreau and D. Volný, Ergodic properties of real cocycles and pseudo-homogeneous Banach spaces, Trans. Amer. Math. Soc. 348 (1996), 4919-4938.
  • [14] V. V. Ryzhikov, The absence of mixing in special flows over rearrangements of segments, Math. Notes 55 (1994), 648-650.
  • [15] K. Schmidt, Cocycles of Ergodic Transformation Groups, Lecture Notes in Math. 1, Mac Millan of India, 1977.
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Bibliografia
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bwmeta1.element.bwnjournal-article-cmv84i1p29bwm
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