Nekhoroshev-stability of \(L4\) and \(L5\) in the spatial restricted three-body problem (Q1302446)

The authors study the Nekhoroshev stability of Lagrangian equilibria \(L4\) and \(L5\) in three-dimensional restricted three-body problem. These equilibria are elliptic for values of the small parameter \(\mu\) up to the Routh's critical mass \(\mu_R \approx 0.0385209\), and are proved to be stable for exponentially long times (i.e.\ Nekhoroshev stable) in the interval \(0<\mu<\mu_R\) with the possible exception of five values of \(\mu\). In order to obtain this result, the authors extend the Nekhoroshev's theorem to the case of directionally quasi-convex Hamiltonians, and also to the case where the Hamiltonians obey a more weakened steepness condition.