Topological entropy of generalized Bunimovich stadium billiards (Q6616681)

The authors generalize their findings in [Pure Appl. Funct. Anal. 6, No. 1, 221--229 (2021; Zbl 1476.37049)] to a much wider class of billiard systems. They construct a subshift of finite type and calculate its topological entropy. Additionally, they demonstrate that the topological entropy of a specific class, denoted by \( (\Sigma_{\ell,N}, \sigma) \) in the paper, is given by the logarithm of the largest root of the equation \( x^2 - 2x - 1 = -2x^{-N}.\) The authors show that the lower limit of the topological entropy of the generalized Bunimovich stadium billiard, as its length \(\ell\) goes to infinity, is at least \(\log(1 + \sqrt{2})\). Furthermore, the authors provide estimates on the entropy of the generalized Bunimovich stadium billiard and the topological entropy of the mushroom billiard.\N\NFor the entire collection see [Zbl 1537.37005].