Linear growth of the derivative for measure-preserving diffeomorphisms
Colloquium Mathematicae (2000)
- Volume: 84/85, Issue: 1, page 147-157
- ISSN: 0010-1354
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Abstract
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topFrączek, Krzysztof. "Linear growth of the derivative for measure-preserving diffeomorphisms." Colloquium Mathematicae 84/85.1 (2000): 147-157. <http://eudml.org/doc/210793>.
@article{Frączek2000,
abstract = {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.},
author = {Frączek, Krzysztof},
journal = {Colloquium Mathematicae},
keywords = {ergodic -diffeomorphism; measure-preserving diffeomorphisms; irrational rotation},
language = {eng},
number = {1},
pages = {147-157},
title = {Linear growth of the derivative for measure-preserving diffeomorphisms},
url = {http://eudml.org/doc/210793},
volume = {84/85},
year = {2000},
}
TY - JOUR
AU - Frączek, Krzysztof
TI - Linear growth of the derivative for measure-preserving diffeomorphisms
JO - Colloquium Mathematicae
PY - 2000
VL - 84/85
IS - 1
SP - 147
EP - 157
AB - 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.
LA - eng
KW - ergodic -diffeomorphism; measure-preserving diffeomorphisms; irrational rotation
UR - http://eudml.org/doc/210793
ER -
References
top- [1] I. P. Cornfeld, S. V. Fomin and Ya. G. Sinai, Ergodic Theory, Springer, Berlin, 1982.
- [2] M. Herman, Sur la conjugaison différentiable des difféomorphismes du cercle à des rotations, Publ. Math. IHES 49 (1979), 5-234.
- [3] A. Iwanik, M. Lemańczyk and D. Rudolph, Absolutely continuous cocycles over irrational rotations, Israel J. Math. 83 (1993), 73-95. Zbl0786.28011
- [4] L. Kuipers and H. Niederreiter, Uniform Distribution of Sequences, Wiley, New York, 1974.
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