  A discontinuous generalization of the standard map, which arises naturally as
the dynamics of a periodically kicked particle in a one dimensional infinite
square well potential, is examined. Existence of competing length scales,
namely the width of the well and the wavelength of the external field,
introduce novel dynamical behaviour. Deterministic chaos induced diffusion is
observed for weak field strengths as the length scales do not match. This is
related to an abrupt breakdown of rotationally invariant curves and in
particular KAM tori. An approximate stability theory is derived wherein the
usual standard map is a point of ``bifurcation''.
