Multifractal analysis for conformal graph directed Markov systems

Mario Roy; Mariusz Urbański

doi:10.3934/dcds.2009.25.627

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2009, Volume 25, Issue 2: 627-650. Doi: 10.3934/dcds.2009.25.627

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Multifractal analysis for conformal graph directed Markov systems

Mario Roy^1, and
Mariusz Urbański^2,

1.
Glendon College, York University, 2275 Bayview Avenue, Toronto
2.
Department of Mathematics, University of North Texas, P.O. Box 311430, Denton, TX 76203-1430

Received: October 2008

Revised: February 2009

Published: June 2009

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Abstract

We derive the multifractal analysis of the conformal measure (or, equivalently, of the invariant measure) associated to a family of weights imposed upon a graph directed Markov system (GDMS) using balls as the filtration. Our analysis is done over a subset of the limit set, a subset which is often large. In particular, this subset is the entire limit set when the GDMS under scrutiny satisfies a boundary separation condition. Our analysis also applies to more general situations such as real and complex continued fractions.

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Mathematics Subject Classification: Primary: 28A80; Secondary: 37C45, 37D35.

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