Multifractal analysis and the variance of Gibbs measures

TM Jordan; M Pollicott

doi:10.1112/jlms/jdm023

Multifractal analysis and the variance of Gibbs measures

TM Jordan, M Pollicott

Research output: Contribution to journal › Article (Academic Journal) › peer-review

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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.

Translated title of the contribution	Multifractal analysis and the variance of Gibbs measures
Original language	English
Pages (from-to)	57 - 72
Number of pages	16
Journal	Journal of the London Mathematical Society
Volume	76 (1)
DOIs	https://doi.org/10.1112/jlms/jdm023
Publication status	Published - Aug 2007

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Publisher: Oxford University Press

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http://jlms.oxfordjournals.org/cgi/content/abstract/76/1/57

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title = "Multifractal analysis and the variance of Gibbs measures",

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.",

author = "TM Jordan and M Pollicott",

note = "Publisher: Oxford University Press",

year = "2007",

month = aug,

doi = "10.1112/jlms/jdm023",

language = "English",

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journal = "Journal of the London Mathematical Society",

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AU - Pollicott, M

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PY - 2007/8

Y1 - 2007/8

N2 - 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.

AB - 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.

U2 - 10.1112/jlms/jdm023

DO - 10.1112/jlms/jdm023

M3 - Article (Academic Journal)

SN - 1469-7750

VL - 76 (1)

SP - 57

EP - 72

JO - Journal of the London Mathematical Society

JF - Journal of the London Mathematical Society

ER -

Multifractal analysis and the variance of Gibbs measures

Abstract

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