arXiv subjects

Tadashi Arimitsu

Publications and source records attributed to Tadashi Arimitsu.

2 recordsLinked to original sources

arXiv2026

On the conformal preimage decay exponent of the Julia sets of rational graph-directed Markov systems

We define and investigate the conformal preimage decay exponent of the Julia sets of rational graph-directed Markov systems. We show that this exponent coincides with the difference between the topological entropy and upper sequential capacity topological pressure for the rational skew product map associated with the system $S$. Here, upper sequential capacity topological pressure is a slight generalisation of upper capacity topological pressure given in \cite{MR969568}.

math.DS↗

arXiv2024

Bowen's formula for a rational graph-directed Markov system

We establish Bowen's formula for the Julia set of a non-elementary, expanding, irreducible and aperiodic rational graph-directed Markov system satisfying the backward separating condition. Towards this end, we shall prove that the associated skew product map is topologically exact on the skew product Julia set, and satisfies the density of repelling periodic points. Moreover, we give a criterion for expandingness in terms of hyperbolicity.

math.DS↗