Aspetti della teoria di regolarizzazione in sistemi della meccanica classica

In classical mechanical system dealing with a gravitational force field, singularities play a dominant role in the global phase portrait. By singularity we mean a point or, a huger set, where the differential equations themselves "blow up" or are otherwise undefined. The behavior of solutions which lead to or even which come close to such a singularity is often quite erratic and is not yet well understood. The subject of study of this thesis is twofold: on the one hand we study how the singularity set affects the behavior of orbits near it. On the other hand, we analyse the possibility of extending solutions beyond the singularity. This second approach is the typical one of the regularization theory.