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Entropy formula for random dynamical systems: relations between entropy, exponents and dimension

Published online by Cambridge University Press:  02 December 2003

MIN QIAN ,
MIN-PING QIAN  and
JIAN-SHENG XIE
MIN QIAN
Affiliation:
School of Mathematical Sciences, Peking University, Beijing 100871, P.R. China (e-mail: jsxie@math.pku.edu.cn)
MIN-PING QIAN
Affiliation:
School of Mathematical Sciences, Peking University, Beijing 100871, P.R. China (e-mail: jsxie@math.pku.edu.cn)
JIAN-SHENG XIE
Affiliation:
School of Mathematical Sciences, Peking University, Beijing 100871, P.R. China (e-mail: jsxie@math.pku.edu.cn)
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Abstract

In this paper we consider random dynamical systems generated by compositions of one-sided independent and identically distributed random diffeomorphisms of class C2 on a compact manifold. We prove an entropy formula for such random dynamical systems without assuming the SRB condition. This result is the random version of the main result obtained by Ledrappier and Young (The metric entropy of diffeomorphisms. Part II: Relations between entropy, exponents and dimension. Ann. Math. 122 (1985), 540–574).

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 23 , Issue 6 , December 2003 , pp. 1907 - 1931
Copyright
2003 Cambridge University Press

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