Abstract. The unlimited energy growth (Fermi acceleration) of a classical particle moving in a billiard with a parameter-dependent boundary oscillating in time is numerically studied. The shape of the boundary is controlled by a parameter and the billiard can change from a focusing one to a billiard with dispersing pieces of the boundary. The complete and simplified versions of the model are considered in the investigation of the conjecture that Fermi acceleration will appear in the time-dependent case when the dynamics is chaotic for the static boundary. Although this conjecture holds for the simplified version, we have not found evidence of Fermi acceleration for the complete model with a breathing boundary. When the breathing symmetry is broken, Fermi acceleration appears in the complete model.

PACS numbers: 05.45.−a, 05.45.Ac, 05.45.Pq

Print publication: Issue 37 (14 September 2007)
Received 21 June 2007, in final form 13 August 2007
Published 29 August 2007