2021/05/30 by Vadim Kaloshin, Kaloshin, V., Comlan Edmond Koudjinan +1
Mathematics · Physics and Astronomy · #2020 numbers: 37C83 #37E40 #37J51 #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.2105.14640
openalex publication_date 2021/05/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In the class of strictly convex smooth boundaries, each of which not having strip around its boundary foliated by invariant curves, we prove that the Taylor coefficients of the "normalized" Mather's β-function are invariants under C^∞-conjugacies. In contrast, we prove that any two elliptic billiard maps are C0-conjugated near their respective boundaries, and C^∞-conjugated in the open cylinder, near the boundary and away from a plain passing through the center of the underlying ellipse. We also prove that if the billiard maps corresponding to two ellipses are topologically conjugated then the two ellipses are similar.