  Classical dynamics is formulated as a Hamiltonian flow on phase space, while
quantum mechanics is formulated as a unitary dynamics in Hilbert space. These
different formulations have made it difficult to directly compare quantum and
classical nonlinear dynamics. Previous solutions have focussed on computing
quantities associated with a statistical ensemble such as variance or entropy.
However a more direct comparison would compare classical predictions to the
quantum for continuous simultaneous measurement of position and momentum of a
single system. In this paper we give a theory of such measurement and show that
chaotic behaviour in classical systems can be reproduced by continuously
measured quantum systems.
