2025/01/27 by Nándor Simányi, Simanyi, Nandor
Mathematics · #37D05 #Advanced Topology and Set Theory #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #advanced mathematical theories
paper · pdf · doi:10.48550/arxiv.2501.16284
openalex publication_date 2025/01/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We investigate the large scale chaotic, topological structure of the trajectories of an infinite sequence of dispersing, hence ergodic, 2D billiards with the configuration space Qn=\mathbbT2 ∖ \bigcupi=0n-1 Di, where the scatterers Di (i=0,1,…,n-1) are disks of radius r<<1 centered at the points (i/n, 0) mod ℤ2. We get effective lower and upper radial bounds for the rotation set R. Furthermore, we also prove the compactness of the admissible rotation set AR and the fact that the rotation vectors v corresponding to admissible periodic orbits form a dense subset of AR. We also obtain asymptotic lower and upper estimates for the sequence htop(n) of topological entropies and precise asymptotic formulas for the metric entropies hμ(n,r).