Asymptotic density of collision orbits in the Restricted Circular Planar 3 Body Problem

Abstract

For the Restricted Circular Planar 3 Body Problem, we show that there exists an open set $\mathcal{U}$ in phase space independent of fixed measure, where the set of initial points which lead to collision is $O({\mu }^{\frac{1}{20}})$ dense as $\mu \to 0$.