Geometry & Topology Seminar: "Chaos and Stability in Umbrella Billiards"

Abstract: Lemon and moon type billiards are families of billiard dynamical systems having the property that, for certain parameters, they show apparent chaotic behavior even though they exhibit neither of the well-known mechanisms for constructing chaotic billiards, dispersing or defocusing. We consider ?umbrella? perturbations of these families, in which one of the two boundary arcs is divided and the curvature of the newly created sub-arcs is varied. For parameters corresponding to non-ergodic lemon and moon billiards, small perturbations may transform elliptic periodic points into a cascade of higher order elliptic points, which either stabilize as the perturbation is increased or dissipate. In the latter case, phase portraits suggest new ergodic examples are created.

Host: Xiang Tang