Linear growth of the derivative for measure-preserving diffeomorphisms
Colloquium Mathematicum, Tome 84 (2000) no. 1, pp. 147-157
Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences
We consider measure-preserving diffeomorphisms of the torus with zero entropy. We prove that every ergodic $C^{1}$-diffeomorphism with linear growth of the derivative is algebraically conjugate to a skew product of an irrational rotation on the circle and a circle $C^{1}$-cocycle. We also show that for no positive β ≠ 1 does there exist an ergodic $C^{2}$-diffeomorphism whose derivative has polynomial growth with degree β.
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author = {Krzysztof Fr\k{a}czek},
title = {Linear growth of the derivative for measure-preserving diffeomorphisms},
journal = {Colloquium Mathematicum},
pages = {147--157},
year = {2000},
volume = {84},
number = {1},
doi = {10.4064/cm-84/85-1-147-157},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/cm-84/85-1-147-157/}
}
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Krzysztof Frączek. Linear growth of the derivative for measure-preserving diffeomorphisms. Colloquium Mathematicum, Tome 84 (2000) no. 1, pp. 147-157. doi: 10.4064/cm-84/85-1-147-157
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