# American Institute of Mathematical Sciences

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

## Multifractal analysis for conformal graph directed Markov systems

 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.
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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