Counting periodic orbits on fractals weighted by their Lyapounov exponents

DOI10.1017/s0013091523000287arXiv2305.16022MaRDI QIDQ6096874

Ugo Bessi

Publication date: 15 September 2023

Published in: Proceedings of the Edinburgh Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2305.16022

zbMATH Keywords

Lyapunov exponentsKusuoka's measurematrix-valued Gibbs measuresperiodic orbits on fractals

Mathematics Subject Classification ID

Random dynamical systems aspects of multiplicative ergodic theory, Lyapunov exponents (37H15) Fractals (28A80) Functional analytic techniques in dynamical systems; zeta functions, (Ruelle-Frobenius) transfer operators, etc. (37C30)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Equilibrium states of the pressure function for products of matrices
• An analogue of the prime number theorem for closed orbits of Axiom A flows
• Dirichlet forms of fractals and products of random matrices
• Ergodic theory of differentiable dynamical systems
• Weyl's problem for the spectral distribution of Laplacians on P.C.F. self-similar fractals
• Another point of view on Kusuoka's measure
• Ergodic theory of Kusuoka measures
• Analysis and Geometry of the Measurable Riemannian Structure on the Sierpiński Gasket
• Ergodic properties of matrix equilibrium states
• The weak Bernoulli property for matrix Gibbs states
• Tauberian theorems