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

Abstract

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.

20 pages, 1 figure

References in corpus (1)

• Limiting modular symbols and their fractal geometry

Cited by in corpus (3)

• The thermodynamic approach to multifractal analysis
• Regularity of multifractal spectra of conformal iterated function systems
• Limiting modular symbols and their fractal geometry