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.
@article{bwmeta1.element.bwnjournal-article-smv125i1p1bwm, author = {W. Bu\l atek and M. Lema\'nczyk and D. Rudolph}, title = {Constructions of cocycles over irrational rotations}, journal = {Studia Mathematica}, volume = {122}, year = {1997}, pages = {1-11}, zbl = {0891.28011}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-smv125i1p1bwm} }
Bułatek, W.; Lemańczyk, M.; Rudolph, D. Constructions of cocycles over irrational rotations. Studia Mathematica, Tome 122 (1997) pp. 1-11. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-smv125i1p1bwm/
[00000] [1] H. Anzai, Ergodic skew product transformations on the torus, Osaka J. Math. 3 (1951), 83-99. | Zbl 0043.11203
[00001] [2] H. Furstenberg, Strict ergodicity and transformations on the torus, Amer. J. Math. 83 (1961), 573-601. | Zbl 0178.38404
[00002] [3] P. Gabriel, M. Lemańczyk et P. Liardet, Ensemble d'invariants pour les produits croisés de Anzai, Mem. Soc. Math. France 119 (1991). | Zbl 0754.28011
[00003] [4] M. Herman, Sur la conjugaison différentiable des difféomorphismes du cercle à des rotations, Publ. IHES 49 (1979), 5-234.
[00004] [5] A. Iwanik, M. Lemańczyk and D. Rudolph, Absolutely continuous cocycles over irrational rotations, Israel J. Math. 83 (1993), 73-95. | Zbl 0786.28011
[00005] [6] A. B. Katok, Constructions in Ergodic Theory, unpublished lecture notes.
[00006] [7] A. V. Kochergin, On the homology of functions over dynamical systems, Dokl. Akad. Nauk SSSR 231 (1976), 795-798. | Zbl 0414.28024
[00007] [8] M. Lemańczyk and Ch. Mauduit, Ergodicity of a class of cocycles over irrational rotations, J. London Math. Soc. 49 (1994), 124-132. | Zbl 0801.28009
[00008] [9] D. Rudolph, and cocycle extensions and complementary algebras, Ergodic Theory Dynam. Systems 6 (1986), 583-599.
[00009] [10] A. Zygmund, Trigonometric Series, Vol. I, Cambridge Univ. Press, 1959. | Zbl 0085.05601