Boltzmann, in his search for an example of a chaotic dynamical system,
studied the planar motion of a particle subject to a central force
bouncing elastically at a line. Gallavotti and Jauslin showed the
system is actually integrable if the force has an inverse-square law. I
will review this and present the new results: the orbits of the
Poincaré map are periodic or quasi-periodic and anisochronous, so that
KAM perturbation theory applies, implying that for small
perturbations the system is still not chaotic. Moreover if for given
values of the integrals of motion one orbit is periodic then all orbits
are periodic. I will review the theory of elliptic curves underlying
these results.
Link per il collegamento: https://meet.google.com/pip-kvzt-fkz
Giovanni Gallavotti