PL EN

Preferencje
Język
Widoczny [Schowaj] Abstrakt
Liczba wyników
Czasopismo

## Fundamenta Mathematicae

2000 | 163 | 2 | 117-130
Tytuł artykułu

### On ergodicity of some cylinder flows

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We study ergodicity of cylinder flows of the form
$T_f:{\sym T}×ℝ → {\sym T}×ℝ$, $T_f(x,y) = (x+α,y+f(x))$,
where $f:{\sym T} → ℝ$ is a measurable cocycle with zero integral. We show a new class of smooth ergodic cocycles. Let k be a natural number and let f be a function such that $D^kf$ is piecewise absolutely continuous (but not continuous) with zero sum of jumps. We show that if the points of discontinuity of $D^kf$ have some good properties, then $T_f$ is ergodic. Moreover, there exists $ε_f > 0$ such that if $v:{\sym T}→ℝ$ is a function with zero integral such that $D^kv$ is of bounded variation with $Var(D^kv) < ε_f$, then $T_{f+v}$ is ergodic.
Słowa kluczowe
Kategorie tematyczne
Czasopismo
Rocznik
Tom
Numer
Strony
117-130
Opis fizyczny
Daty
wydano
2000
otrzymano
1998-11-16
Twórcy
autor
• Faculty of Mathematics and Computer, Science Nicholas Copernicus University, Chopina 12/18, 87-100 Toruń, Poland
Bibliografia
• [1] I. P. Cornfeld, S. V. Fomin and Ya. G. Sinai, Ergodic Theory, Springer, Berlin, 1982.
• [2] H. Furstenberg, Strict ergodicity and transformations on the torus, Amer. J. Math. 83 (1961), 573-601.
• [3] P. Gabriel, M. Lemańczyk et P. Liardet, Ensemble d'invariants pour les produits croisés de Anzai, Mém. Soc. Math. France 47 (1991).
• [4] P. Hellekalek and G. Larcher, On the ergodicity of a class of skew products, Israel J. Math. 54 (1986), 301-306.
• [5] M. R. Herman, Sur la conjugaison différentiable des difféomorphismes du cercle à des rotations, Publ. Mat. IHES 49 (1979), 5-234.
• [6] 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.
• [7] W. Parry, Topics in Ergodic Theory, Cambridge Univ. Press, Cambridge, 1981.
• [8] D. Pask, Skew products over the irrational rotation, Israel J. Math. 69 (1990), 65-74.
• [9] D. Pask, Ergodicity of certain cylinder flows, ibid. 76 (1991), 129-152.
• [10] K. Schmidt, Cocycles of Ergodic Transformation Groups, Macmillan Lectures in Math. 1, Delhi, 1977.
Typ dokumentu
Bibliografia
Identyfikatory