Nathan Dalaklis

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20212026

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math.GN2024

The $D$ -Variant of Transfinite Hausdorff Dimension

Bryce Decker, Nathan Dalaklis

We assign every metric space $X$ the value $t_{D} H D (X)$ , an ordinal number or one of the symbols $- 1$ or $Ω$ , and we call it the $D$ -variant of transfinite Hausdorff dimension of $…

math.DS2024

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

Nathan Dalaklis

Let $Φ = {ϕ_{e}}_{e \in E}$ be a finitely irreducible conformal graph directed Markov system (CGDMS) with symbolic representation $E_{A}^{\infty}$ and limit set $J$ . Under a mild condi…

The D-Variant of Transfinite Hausdorff Dimension

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

The $D$ -Variant of Transfinite Hausdorff Dimension