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• # Artykuł - szczegóły

## Colloquium Mathematicum

2004 | 99 | 1 | 75-90

## On diffeomorphisms with polynomial growth of the derivative on surfaces

EN

### Abstrakty

EN
We consider zero entropy $C^{∞}$-diffeomorphisms on compact connected $C^{∞}$-manifolds. We introduce the notion of polynomial growth of the derivative for such diffeomorphisms, and study it for diffeomorphisms which additionally preserve a smooth measure. We show that if a manifold M admits an ergodic diffeomorphism with polynomial growth of the derivative then there exists a smooth flow with no fixed point on M. Moreover, if dim M = 2, then necessarily M = 𝕋² and the diffeomorphism is $C^{∞}$-conjugate to a skew product on the 2-torus.

75-90

wydano
2004

### Twórcy

autor
• Faculty of Mathematics and Computer Science, Nicolaus Copernicus University, Chopina 12/18, 87-100 Toruń, Poland