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Multifractal analysis and the variance of Gibbs measures
Author(s) -
Jordan T.,
Pollicott M.
Publication year - 2007
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/jlms/jdm023
Subject(s) - multifractal system , decomposition , variance (accounting) , mathematics , convergence (economics) , variance decomposition of forecast errors , gibbs measure , econometrics , statistical physics , statistics , fractal , economics , mathematical analysis , physics , chemistry , accounting , organic chemistry , economic growth
ABSTRACT The multifractal decomposition of Gibbs measures for a conformal iterated function system is well known. We look at a finer decomposition which also takes into account the rate of convergence. This is motivated by the work of Olsen in the self‐similar case. Our study of this finer decomposition involves investigation of the variance of Gibbs measures. This is a problem of independent interest.