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

2025/07/24 by Yuya Arima, Arima, Yuya · 1 citation
Computer Science · Mathematics · Physics and Astronomy · #Chaos control and synchronization #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Neural Networks Stability and Synchronization

paper · pdf · doi:10.48550/arxiv.2507.18041

openalex publication_date 2025/07/24 · openalex created_date 2025/10/16 · openalex updated_date 2026/07/30

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.

Citations

• Multifractal analysis of random weak Gibbs measures
• The Lyapunov spectrum of some parabolic systems

Cited by

• Bowen's formula and the difference between random iterated function systems and random recursive constructions

Related

• Multifractal Analysis of F-exponents for Finitely Irreducible Conformal Graph Directed Markov Systems
• Multifractal analysis for conformal graph directed Markov systems
• On fast Lyapunov spectra for Markov-Rényi maps
• Conformal Graph Directed Markov Systems
• The relation between quenched and annealed Lyapunov exponents in random\n potential on trees