  The Gross Pitaevski map is a discrete time, split operator version of the
Gross Pitaevski dynamics in the circle, for which exponential instability has
been recently reported. Here it is studied as a classical dynamical system in
its own right. A systematic analysis of Lyapunov exponents exposes strongly
chaotic behavior. Exponential growth of energy is then shown to be a direct
consequence of rotational invariance and for stationary solutions the full
spectrum of Lyapunov exponents is analytically computed. The present analysis
includes the resonant case, when the free rotation period is commensurate to
$2\pi$, and the map has countably many constants of the motion. Except for
lowest order resonances, this case exhibits an integrable-chaotic transition.
