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arXiv · 2404.09348

Multifractal Analysis of F-exponents for Finitely Irreducible Conformal Graph Directed Markov Systems

Nathan Dalaklis
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Abstract

Let $\Phi = \{\phi_e\}_{e\in E}$ be a finitely irreducible conformal graph directed Markov system (CGDMS) with symbolic representation $E_A^{\infty}$ and limit set $J$. Under a mild condition on the system, we give a multifractal analysis of level sets of Birkhoff averages with respect to Hausdorff dimension for a large family of functions. We then apply these results to a few examples in the case of both $E$ finite and $E$ countably infinite.

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Nathan Dalaklis. 2024-04-14. Multifractal Analysis of F-exponents for Finitely Irreducible Conformal Graph Directed Markov Systems. https://arxiv.org/abs/2404.09348

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