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Vanishing transverse entropy in smooth ergodic theory

Published online by Cambridge University Press:  27 September 2010

FRANÇOIS LEDRAPPIER  and
JIAN-SHENG XIE
FRANÇOIS LEDRAPPIER
Affiliation:
LPMA, UMR 7599, Boǐte courrier 188, Université Paris VI, 4 Place Jussieu, 75252 Paris Cedex 05, France (email: francois.ledrappier@upmc.fr)
JIAN-SHENG XIE
Affiliation:
School of Mathematical Sciences, Fudan University, Shanghai 200433, PR China (email: jiansheng.xie@gmail.com)
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Abstract

For a measure-preserving transformation, the entropy being zero means that there is no increasing σ-algebra. In this note, we prove that a similar phenomenon occurs for C2 diffeomorphisms when considering the increment between the partial entropies associated with different exponents.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 31 , Issue 4 , August 2011 , pp. 1229 - 1235
Copyright
Copyright © Cambridge University Press 2010

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