title: One-particle and few-particle billiards.
abstract: We study the dynamics of one-particle and few-particle billiard systems in containers of various shapes. In few-particle systems, the particles collide elastically both against the boundary and against each other. In the one-particle case, we investigate the formation and destruction of resonance islands in (generalized) mushroom billiards, which are a recently discovered class of Hamiltonian systems with mixed regular-chaotic dynamics. In the few-particle case, we compare the dynamics in container geometries whose counterpart one-particle billiards are integrable, chaotic, and mixed. One of our findings is that two-, three-, and four-particle billiards confined to containers with integrable one-particle counterparts inherit some integrals of motion and exhibit a regular partition of phase space into ergodic components of positive measure. Therefore, the shape of a container matters not only for noninteracting particles but also for interacting particles.
authors.affiliation: School of Electrical and Computer Engineering and School of Mathematics, Georgia Institute of Technology, Atlanta, Georgia 30332-0160, USA.
authors.forename: Steven
authors.initials: S
authors.lastname: Lansel
authors.forename: Mason A
authors.initials: MA
authors.lastname: Porter
authors.forename: Leonid A
authors.initials: LA
authors.lastname: Bunimovich