Multifractal analysis of the Lyapunov exponent for random graph directed Markov systems
Dynamical Systems
2026-01-16 v1
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.
Keywords
Cite
@article{arxiv.2507.18041,
title = {Multifractal analysis of the Lyapunov exponent for random graph directed Markov systems},
author = {Yuya Arima},
journal= {arXiv preprint arXiv:2507.18041},
year = {2026}
}
Comments
24 pages