On diffeomorphisms with polynomial growth of the derivative on surfaces

• Autorzy: Krzysztof Frączek
• Języki publikacji: 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.

Kategorie tematyczne

• 37C40: Smooth ergodic theory, invariant measures
• 37C05: Smooth mappings and diffeomorphisms
• 37A05: Measure-preserving transformations

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2004
• Tom: 99
• Numer: 1
• Strony: 75-90

Daty

wydano

2004

Twórcy

autor

Krzysztof Frączek

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

Identyfikatory

DOI

10.4064/cm99-1-8