  Defocusing mechanism provides a way to construct chaotic (hyperbolic)
billiards with focusing components by separating all regular components of the
boundary of a billiard table sufficiently far away from each focusing
component. If all focusing components of the boundary of the billiard table are
circular arcs, then the above separation requirement reduces to that all
circles obtained by completion of focusing components are contained in the
billiard table. In the present paper we demonstrate that a class of convex
tables--asymmetric lemons, whose boundary consists of two circular arcs,
generate hyperbolic billiards. This result is quite surprising because the
focusing components of the asymmetric lemon table are extremely close to each
other, and because these tables are perturbations of the first convex ergodic
billiard constructed more than forty years ago.
