FINDING REGULAR ORBITS

A general method is presented to determine regular orbits in the presence of irregular trajectories in phase space for a dynamical system of n degrees of freedom. A cost functional is introduced with a control field to guide the system towards regular orbits. Iteration of the optimizing algorithm naturally seeks out regular orbits with the control field turned off. If the system is completely chaotic in some region, the method chooses the best initial condition to achieve a nearly regular orbit. An illustration is presented for n = 3 and n = 4 dimensional dynamical systems.