Constructions of cocycles over irrational rotations

W. Bułatek; M. Lemańczyk; D. Rudolph

ArticleOriginal scientific text

Title

Constructions of cocycles over irrational rotations

Authors ¹, ¹, ²

Affiliations

Department of Mathematics and Computer Science, Nicholas Copernicus University, Chopina 12/18, 87-100 Toruń, Poland
Department of Mathematics, University of Maryland, College Park, Maryland 20742, U.S.A.

Abstract

We construct a coboundary cocycle which is of bounded variation, is homotopic to the identity and is Hölder continuous with an arbitrary Hölder exponent smaller than 1.

H. Anzai, Ergodic skew product transformations on the torus, Osaka J. Math. 3 (1951), 83-99.
H. Furstenberg, Strict ergodicity and transformations on the torus, Amer. J. Math. 83 (1961), 573-601.
P. Gabriel, M. Lemańczyk et P. Liardet, Ensemble d'invariants pour les produits croisés de Anzai, Mem. Soc. Math. France 119 (1991).
M. Herman, Sur la conjugaison différentiable des difféomorphismes du cercle à des rotations, Publ. IHES 49 (1979), 5-234.
A. Iwanik, M. Lemańczyk and D. Rudolph, Absolutely continuous cocycles over irrational rotations, Israel J. Math. 83 (1993), 73-95.
A. B. Katok, Constructions in Ergodic Theory, unpublished lecture notes.
A. V. Kochergin, On the homology of functions over dynamical systems, Dokl. Akad. Nauk SSSR 231 (1976), 795-798.
M. Lemańczyk and Ch. Mauduit, Ergodicity of a class of cocycles over irrational rotations, J. London Math. Soc. 49 (1994), 124-132.
D. Rudolph, $ℤ^{n}$ and $ℕ^{n}$ cocycle extensions and complementary algebras, Ergodic Theory Dynam. Systems 6 (1986), 583-599.
A. Zygmund, Trigonometric Series, Vol. I, Cambridge Univ. Press, 1959.

Title

Constructions of cocycles over irrational rotations

Affiliations

Abstract

Bibliography