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Billiards with singular invariant curves
Stefano Baranzini
We investigate the regularity of invariant curves of rotation number for a special class of symplectic twist maps of the annulus, billiard maps. We construct strictly convex…
Non-integrability of n-centre billiards
Stefano Baranzini
We investigate a class of mechanical billiards, where a particle moves in a planar region under the influence of an n-centre potential and reflects elastically on a straight wall.…
Mountain pass frozen planet orbits in the helium atom model
Stefano Baranzini, Gian Marco Canneori, Susanna Terracini
We seek frozen planet orbits for the helium atom through an application of the Mountain Pass Lemma to the Lagrangian action functional. Our method applies to a wide class of gravit…
Chaotic phenomena for generalised N-centre problems
Stefano Baranzini, Gian Marco Canneori
We study a class of singular dynamical systems which generalise the classical N-centre problem of Celestial Mechanics to the case in which the configuration space is a Riemannian s…
Morse index of circular solutions for attractive central force problems on surfaces
Stefano Baranzini, Alessandro Portaluri, Ran Yang
The classical theory of attractive central force problem on the standard (flat) Euclidean plane can be generalized to surfaces by reformulating the basic underlying physical princi…