Multifractal analysis of the Lyapunov exponent for random graph directed Markov systems

TL;DR

This paper conducts a multifractal analysis of the Lyapunov exponent in random conformal graph directed Markov systems and generalizes Bowen's formula for their limit sets.

Contribution

It introduces new refined properties of random finitely primitive countable Markov shifts and extends Bowen's formula to these systems.

Findings

Multifractal spectrum of the Lyapunov exponent characterized.

Generalization of Bowen's formula for random conformal systems.

Enhanced understanding of the structure of limit sets in these systems.

Abstract

In this paper, we perform the multifractal analysis of the Lyapunov exponent for random conformal graph directed Markov systems introduced by Roy and Urba\'nski (2011). We also generalize Bowen's formula for the limit set of a random conformal graph directed Markov system established by Roy and Urba\'nski. To do this, we develop several refined properties of random finitely primitive countable Markov shifts.