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Multifractal analysis for disintegrations of Gibbs measures and conditional Birkhoff averages

Published online by Cambridge University Press:  01 June 2009

DE-JUN FENG  and
LIN SHU
DE-JUN FENG
Affiliation:
Department of Mathematics, The Chinese University of Hong Kong, Shatin, Hong Kong Department of Mathematical Sciences, Tsinghua University, Beijing 100084, People’s Republic of China (email: djfeng@math.cuhk.edu.hk)
LIN SHU
Affiliation:
School of Mathematical Sciences, Peking University, Beijing 100871, People’s Republic of China (email: lshu@math.pku.edu.cn)
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Abstract

The paper is devoted to the study of the multifractal structure of disintegrations of Gibbs measures and conditional (random) Birkhoff averages. Our approach is based on the relativized thermodynamic formalism, convex analysis and, especially, the delicate constructions of Moran-like subsets of level sets.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 29 , Issue 3 , June 2009 , pp. 885 - 918
Copyright
Copyright © Cambridge University Press 2009

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