Multifractal analysis for conformal graph directed Markov systems

Details Multifractal analysis for conformal graph directed Markov systems Multifractal analysis for conformal graph directed Markov systems

2008-09-25

arxiv.org/abs/0809.4436v1

Mathematics

Dynamical Systems

26 pages

Scientific paper

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

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