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arXiv · 2507.18041

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

Yuya Arima
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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.

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Yuya Arima. 2025-07-24. Multifractal analysis of the Lyapunov exponent for random graph directed Markov systems. https://doi.org/10.3934/dcds.2026009

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