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July  2009, 25(2): 627-650. doi: 10.3934/dcds.2009.25.627

Multifractal analysis for conformal graph directed Markov systems

Mario Roy 1, and  Mariusz Urbański 2,

1. 

Glendon College, York University, 2275 Bayview Avenue, Toronto, Canada
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

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.
Keywords: Multifractal analysis, real and complex continued fractions., graph directed Markov systems, thermodynamic formalism, conformal maps.
Mathematics Subject Classification: Primary: 28A80; Secondary: 37C45, 37D3.
Citation: Mario Roy, Mariusz Urbański. Multifractal analysis for conformal graph directed Markov systems. Discrete and Continuous Dynamical Systems, 2009, 25 (2) : 627-650. doi: 10.3934/dcds.2009.25.627
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