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Measure-preserving diffeomorphisms of the torus

Published online by Cambridge University Press:  28 November 2001

KRZYSZTOF FRĄCZEK
KRZYSZTOF FRĄCZEK
Affiliation:
Faculty of Mathematics and Computer Science, Nicholas Copernicus University, ul. Chopina 12/18, 87-100 Toruń, Poland (e-mail: [email protected])
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Abstract

We consider measure-preserving diffeomorphisms of the two-dimensional torus with zero entropy. We prove that every ergodic C^3-diffeomorphism f of the two-dimensional torus with linear growth of the derivative (i.e. the sequence \{n^{-1}Df^n\}_{n\in{\mathbb N}} is uniformly separated from 0 and \infty and it is bounded in the C^2-norm) is algebraically conjugate to a skew product of an irrational rotation on the circle and a circle C^3-cocycle with non-zero topological degree.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 21 , Issue 6 , December 2001 , pp. 1759 - 1781
Copyright
2001 Cambridge University Press

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