We consider measure-preserving diffeomorphisms of the torus with zero entropy. We prove that every ergodic -diffeomorphism with linear growth of the derivative is algebraically conjugate to a skew product of an irrational rotation on the circle and a circle -cocycle. We also show that for no positive β ≠ 1 does there exist an ergodic -diffeomorphism whose derivative has polynomial growth with degree β.
@article{bwmeta1.element.bwnjournal-article-cmv84i1p147bwm,
author = {Krzysztof Fr\k aczek},
title = {Linear growth of the derivative for measure-preserving diffeomorphisms},
journal = {Colloquium Mathematicae},
volume = {84/85},
year = {2000},
pages = {147-157},
zbl = {0976.37001},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-cmv84i1p147bwm}
}
Frączek, Krzysztof. Linear growth of the derivative for measure-preserving diffeomorphisms. Colloquium Mathematicae, Tome 84/85 (2000) pp. 147-157. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-cmv84i1p147bwm/
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