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October 17, 2025Open Access

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

Key Points

The analysis identifies multifractal properties associated with the Lyapunov exponent in random graphs.
Refined properties of finitely primitive countable Markov shifts enhance understanding of these systems.
Generalizations of Bowen's formula for limit sets contribute significantly to the field of random systems.
This work extends existing frameworks for analyzing time evolution in directed Markov 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 Urbański (2011). We also generalize Bowen's formula for the limit set of a random conformal graph directed Markov system established by Roy and Urbański. To do this, we develop several refined properties of random finitely primitive countable Markov shifts.

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Cite This Study

Y. Arima (Thu,) studied this question.

synapsesocial.com/papers/68f19f20de32064e504dde57 https://doi.org/https://doi.org/10.48550/arxiv.2507.18041

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