On diffeomorphisms with polynomial growth of the derivative on surfaces

Krzysztof Frączek. "On diffeomorphisms with polynomial growth of the derivative on surfaces." Colloquium Mathematicae 99.1 (2004): 75-90. <http://eudml.org/doc/284594>.

@article{KrzysztofFrączek2004,
abstract = {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 = ² and the diffeomorphism is $C^\{∞\}$-conjugate to a skew product on the 2-torus.},
author = {Krzysztof Frączek},
journal = {Colloquium Mathematicae},
keywords = {zero entropy -diffeomorphisms; polynomial growth of the derivative; measure-preserving diffeomorphisms},
language = {eng},
number = {1},
pages = {75-90},
title = {On diffeomorphisms with polynomial growth of the derivative on surfaces},
url = {http://eudml.org/doc/284594},
volume = {99},
year = {2004},
}

TY - JOUR
AU - Krzysztof Frączek
TI - On diffeomorphisms with polynomial growth of the derivative on surfaces
JO - Colloquium Mathematicae
PY - 2004
VL - 99
IS - 1
SP - 75
EP - 90
AB - 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 = ² and the diffeomorphism is $C^{∞}$-conjugate to a skew product on the 2-torus.
LA - eng
KW - zero entropy -diffeomorphisms; polynomial growth of the derivative; measure-preserving diffeomorphisms
UR - http://eudml.org/doc/284594
ER -