We consider zero entropy -diffeomorphisms on compact connected -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 = ² and the diffeomorphism is -conjugate to a skew product on the 2-torus.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-cm99-1-8,
author = {Krzysztof Fr\k aczek},
title = {On diffeomorphisms with polynomial growth of the derivative on surfaces},
journal = {Colloquium Mathematicae},
volume = {100},
year = {2004},
pages = {75-90},
zbl = {1048.37016},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm99-1-8}
}
Krzysztof Frączek. On diffeomorphisms with polynomial growth of the derivative on surfaces. Colloquium Mathematicae, Tome 100 (2004) pp. 75-90. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm99-1-8/