Regularisation by Hamiltonian extension

Abstract

We consider the Kepler potential and its relatives $q\mapsto -\Vert q{\Vert }^{-2(1-1/n)}$, $n\in \mathbb{N}$ in arbitrary dimension $d$. We derive a unique real-analytic symplectic extension of phase space on which the Hamiltonian flow is complete and still real-analytic.