Linear growth of the derivative for measure-preserving diffeomorphisms

Volume 84 / 2000

Krzysztof Frączek Colloquium Mathematicum 84 (2000), 147-157 DOI: 10.4064/cm-84/85-1-147-157


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.


  • Krzysztof Frączek

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