2025/12/03 by David Burguet, Burguet, David, Chiyi Luo +3
Mathematics · Physics and Astronomy · #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric and Algebraic Topology #Mathematical Dynamics and Fractals #Quantum chaos and dynamical systems
paper · pdf · doi:10.48550/arxiv.2512.03515
openalex publication_date 2025/12/03 · openalex created_date 2025/12/05 · openalex updated_date 2026/07/28
In this paper, we prove that ergodic measures with large entropy give uniformly large measure to the set of points with simultaneously long unstable and long stable manifolds. As a consequence, for C∞ surface diffeomorphisms, we establish an effective version of the SPR property. For C∞ three-dimensional flows without singularities, we prove the finiteness of equilibrium measures for admissible potentials whose variation is strictly less than half of the topological entropy.