2023/05/25 by Ugo Bessi, Bessi, Ugo
Mathematics · Physics and Astronomy · #Dynamical Systems (math.DS) #FOS: Mathematics #Markov Chains and Monte Carlo Methods #Mathematical Dynamics and Fractals #Theoretical and Computational Physics
paper · pdf · doi:10.48550/arxiv.2305.16022
openalex publication_date 2023/05/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Several authors have shown that Kusuoka's measure κ on fractals is a scalar Gibbs measure; in particular, it maximises a pressure. There is also a different approach, in which one defines a matrix-valued Gibbs measure μ which induces both Kusuoka's measure κ and Kusuoka's bilinear form. In the first part of the paper we show that one can define a "pressure" for matrix valued measures; this pressure is maximised by μ. In the second part, we use the matrix-valued Gibbs measure μ to count periodic orbits on fractals, weighted by their Lyapounov exponents.