Billiards in the ZP Unit Balls of the Plane
نویسنده
چکیده
We study a one-parameter family of billiard maps Tp given by the convex tables j.rIP + IyIP = 1 for p E [l, m]. We note that the topological entropy is positive if p $ {l, 2, a}. We study the linear stability of some periodic orbits and observe that the stability of these orbits changes for p = 2. For p $ { 1, 2, m}, there exist elliptic periodic orbits suggesting that Tp is not ergodic for all p. We compute numerically the metric entropy of the maps TP in the interval [l, 121 and the limiting behavior near p = 2.
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