title: Ergodicity of the generalized lemon billiards.
abstract: In this paper, we study a two-parameter family of convex billiard tables, by taking the intersection of two round disks (with different radii) in the plane. These tables give a generalization of the one-parameter family of lemon-shaped billiards. Initially, there is only one ergodic table among all lemon tables. In our generalized family, we observe numerically the prevalence of ergodicity among the some perturbations of that table. Moreover, numerical estimates of the mixing rate of the billiard dynamics on some ergodic tables are also provided.
authors.affiliation: Department of Computer Science, University of Illinois at Urbana-Champaign, Champaign, Illinois 61801-2302, USA.
authors.forename: Jingyu
authors.initials: J
authors.lastname: Chen
authors.affiliation: Department of Mathematics and Statistics, UMass Amherst, Amherst, Massachusetts 01003, USA.
authors.forename: Luke
authors.initials: L
authors.lastname: Mohr
authors.affiliation: Department of Mathematics and Statistics, UMass Amherst, Amherst, Massachusetts 01003, USA.
authors.forename: Hong-Kun
authors.initials: HK
authors.lastname: Zhang
authors.affiliation: Department of Mathematics and Statistics, UMass Amherst, Amherst, Massachusetts 01003, USA.
authors.forename: Pengfei
authors.initials: P
authors.lastname: Zhang