Alessandro Portaluri, University of Turin
"Existence and Stability Results in Celestial Mechanics"
Is the solar system stable? This is maybe one of the oldest open questions in dynamical systems. It is still a lively and very active research field starting from Newton, Lagrange, Maxwell, Poincar\'e and Birkhoff (only to mention a few) who proved several astonishing results in this direction.
A lot of useful techniques to tackle this problem were developed during the last decades: KAM theory, symplectic and contact methods, interval arithmetic, etc. One more (variationally oriented) piece we add to this arsenal: the index theory!
In this talk we introduce some new ideas behind many recent results on this topic and we discuss some new perspectives and challenges on singular (weak force) Lagrangian problems. We show the existence of equivariant periodic orbits and we show some recent (in)stability results for a plethora of periodic motions via symplectic techniques.
MC 5403