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Linear growth of the derivative for measure-preserving diffeomorphisms

Krzysztof Frączek (2000)

Colloquium Mathematicae

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.

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