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A new entropy formula of Ledrappier–Young type for linear toral dynamics

Published online by Cambridge University Press:  05 December 2012

JIAN-SHENG XIE
JIAN-SHENG XIE*
Affiliation:
School of Mathematical Sciences, Fudan University, Shanghai 200433, PR China (email: jiansheng.xie@gmail.com)
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Abstract

A detailed Ledrappier–Young theory is presented for linear toral dynamics. First, a proof is given for a simplified definition for local entropies which holds in more general settings besides the current linear dynamics. Then it is shown that the transverse dimensions can be defined directly via the Smale structure of the linear dynamical system. A new entropy formula of Ledrappier–Young type is obtained. The conjecture of Ledrappier and Xie [Vanishing transverse entropy in smooth ergodic theory. Ergod. Th. & Dynam. Sys. 31(4) (2011), 1229–1235] is also discussed for such linear dynamics.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 34 , Issue 3 , June 2014 , pp. 1037 - 1054
Copyright
©2012 Cambridge University Press 

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