Session S03 - Geometric and Variational Methods in Celestial Mechanics

Monday, July 12, 15:00 ~ 15:25 UTC-3

The anisotropic $N$-centre problem

Gian Marco Canneori

Università di Torino, Italy   -   This email address is being protected from spambots. You need JavaScript enabled to view it.

We consider an anisotropic version of the planar $N$-centre problem of Celestial Mechanics and we prove the existence of symbolic dynamics on constant negative energy shells. The proof relies on a broken geodesics technique, where trajectories are extremals for the Maupertuis' functional. A deep analysis of collision trajectories reveals also to be essential in this context. Close to every centre, minimal collision arcs span the local stable manifold of an equilibrium point lying in the McGehee collision manifold.

Joint work with Vivina Barutello (Università di Torino) and Susanna Terracini (Università di Torino).

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