  Sharkovskii proved that the existence of a periodic orbit in a
one-dimensional dynamical system implies existence of infinitely many periodic
orbits. We obtain an analog of Sharkovskii's theorem for periodic orbits of
shear homeomorphisms of the torus. This is done by obtaining a dynamical order
relation on the set of simple orbits and simple pairs. We then use this order
relation for a global analysis for a quantum chaotic physical system called the
kicked accelerated particle.
