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

Published 24 Jul 2025 in math.DS | (2507.18041v1)

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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