  A family of discontinuous symplectic maps on the cylinder is considered. This
family arises naturally in the study of nonsmooth Hamiltonian dynamics and in
switched Hamiltonian systems. The transformation depends on two parameters and
is a canonical model for the study of bounded and unbounded behavior in
discontinuous area-preserving mappings due to nonlinear resonances. This paper
provides a general description of the map and points out its connection with
another map considered earlier by Kesten. In one special case, an unbounded
orbit is explicitly constructed.
