Separation coordinates in Hénon-Heiles systems
Source of Publication
Physics Letters, Section A: General, Atomic and Solid State Physics
© 2019 Elsevier B.V. In this paper we apply the method of the Kowalewski's Conditions to separate the seven Hénon-Heiles integrable systems. For each of them we provide explicitly the separation coordinates in the form of eigenvalues of a matrix M called Control Matrix. A couple of systems (HH3 KK and HH4 1:12:16) are presented and discussed in a more general form than usually in the literature. We show that the process of separation of coordinates can be reduced, at the end, to the choice of a single function and, eventually, a vector field transversal to the Lagrangian foliation in an extended phase space.
Sottocornola, Nicola, "Separation coordinates in Hénon-Heiles systems" (2019). Scopus Indexed Articles. 467.