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A technique for reducing the number of integrals in a Monte Carlo calculationis introduced. For integrations relying on classical or mean-field trajectorieswith local weighting functions, it is possible to integrate analytically atleast half of the integration variables prior to setting up the particularMonte Carlo calculation of interest, in some cases more. Proper accounting ofinvariant phase space structures shows the system's dynamics is reducible intocomposite stable and unstable degrees of freedom. Stable degrees of freedombehave locally in the reduced dimensional phase space exactly as an analogousintegrable system would. Classification of the unstable degrees of freedom isdependent upon the degree of chaos present in the dynamics. The techniques forderiving the requisite canonical coordinate transformations are developed andshown to block diagonalize the stability matrix into irreducible parts. Indoing so, it is demonstrated how to reduce the amount of sampling directionsnecessary in a Monte Carlo simulation. The technique is illustrated bycalculating return probabilities and expectation values for different dynamicalregimes of a two-degree-of-freedom coupled quartic oscillator within aclassical Wigner method framework.

A Reduced Dimensional Monte Carlo Method: Preliminary Integrations