Partial control and avoidance of escape from a potential well

Abstract eng:
In this work, we present application of geometric and topological approaches of phase space transport to dynamical systems which exhibit transition out of a potential well or escape from the realm of bounded motion. This phenomena is observed in problems of celestial mechanics, chemical kinetics and ship dynamics where by transition and escape may be beneficial or detrimental. We present results in the context of mechanical systems that can be geometrically reduced to two-dimensional maps using invariant manifolds of unstable periodic orbits and suitable Poincar´e surfaces-of-section. We apply a recently developed notion of controlling a dynamical system, in the presence of a random bounded disturbance while applying a smaller control, to avoid transition and escape into an undesirable realm of phase space.

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