2022/12/19 by Malo Jézéquel, Jézéquel, Malo
Mathematics · Physics and Astronomy · #37C30 #37D20 #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Mathematical Dynamics and Fractals #Quantum chaos and dynamical systems
paper · pdf · doi:10.48550/arxiv.2212.09881
openalex publication_date 2022/12/19 · openalex created_date 2023/01/04 · openalex updated_date 2026/07/28
We prove an upper bound for the number of Ruelle resonances for Koopman operators associated to real-analytic Anosov diffeomorphisms: in dimension d, the number of resonances larger than r is a O(|log r|d) when r goes to 0. For each connected component of the space of real-analytic Anosov diffeomorphisms on a real-analytic manifold, we prove a dichotomy: either the exponent d in our bound is never optimal, or it is optimal on a dense subset. Using examples constructed by Bandtlow, Just and Slipantschuk, we see that we are always in the latter situation for connected components of the space of real-analytic Anosov diffeomorphisms on the 2-dimensional torus.