Linear growth of the derivative for measure-preserving diffeomorphisms

• Autorzy: Krzysztof Frączek
• Języki publikacji: EN

Abstrakty

EN

We consider measure-preserving diffeomorphisms of the torus with zero entropy. We prove that every ergodic $C^{1}$-diffeomorphism with linear growth of the derivative is algebraically conjugate to a skew product of an irrational rotation on the circle and a circle $C^{1}$-cocycle. We also show that for no positive β ≠ 1 does there exist an ergodic $C^{2}$-diffeomorphism whose derivative has polynomial growth with degree β.

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2000
• Tom: 84/85
• Numer: 1
• Strony: 147-157

Daty

wydano

2000

otrzymano

1999-05-31

poprawiono

1999-08-27

Twórcy

autor

Krzysztof Frączek

• 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] M. Herman, Sur la conjugaison différentiable des difféomorphismes du cercle à des rotations, Publ. Math. IHES 49 (1979), 5-234.
• [3] A. Iwanik, M. Lemańczyk and D. Rudolph, Absolutely continuous cocycles over irrational rotations, Israel J. Math. 83 (1993), 73-95.
• [4] L. Kuipers and H. Niederreiter, Uniform Distribution of Sequences, Wiley, New York, 1974.