Higher-dimensional multifractal value sets for conformal infinite graph directed Markov systems

Details Higher-dimensional multifractal value sets for conformal infinite graph directed Markov systems Higher-dimensional multifractal value sets for conformal infinite graph directed Markov systems

2007-01-19

arxiv.org/abs/math/0701541v2

Nonlinearity 20 (2007), no. 8, pp. 1969-1985

Mathematics

Dynamical Systems

20 pages, 1 figure

Scientific paper

10.1088/0951-7715/20/8/009

We give a description of the level sets in the higher dimensional multifractal formalism for infinite conformal graph directed Markov systems. If these systems possess a certain degree of regularity this description is complete in the sense that we identify all values with non-empty level sets and determine their Hausdorff dimension. This result is also partially new for the finite alphabet case.

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