Periodic motions plays a decisive role in understanding the qualitative behaviour of Hamiltonian systems. Indeed, starting from the monumental monograph of Poincaré on celestial mechanics, it has become increasingly clear that periodic orbits can be responsible both for local stability (elliptic orbits), and for chaotic phenomena (hyperbolic orbits). One hundred years after Poincaré, work of Hofer-Wysocki-Zehnder and of Dell'Antonio-D'Onofrio-Ekeland have provided crucial information about the existence and the type of periodic orbits for the important class of convex systems. In the last part of the talk, I will discuss how these results can be applied to a concrete case: the motion of a charged particle on the two-sphere under the effect of a magnetic field.
Montag, den 24. Juli 2017 um 10:40 Uhr, in Mathematikon , SR 3 Montag, den 24. Juli 2017 at 10:40, in Mathematikon , SR 3