Studio sulla regolarizzazione di collisioni nel problema degli n-corpi.

The thesis concerns the regularisation of collisions in Kepler n-body problem (both unperturbed and perturbed) from different mathematical points of view. The Levi-Civita regularisation is presented as a fundamental theory in this field; moreover, its generalisation in three-dimensional space is studied, elaborated by P. Kustaanheimo and E. Stiefel. The Birkhoff regularisation and its generalisation (the so-called B3 regularisation) is also presented, which is very useful in the simultaneous regularisation of both collisions that characterised the problem, an unique property not applicable in the first two regularisations. Subsequently, a purely algebraic regularisation is studied using quaternions, a theory developed by Waldvogel. The use of quaternions simplifies the problem in a considerable way. Furthermore, a regularisation using variational theories is also analysed; it is the so-called "Averaging Method" on a manifold, developed by Moser for both the unperturbed and perturbed Kepler problems. Finally, a purely geometric regularisation is presented, namely the "Regularisation of Vector Fields by Surgery" studied by Easton.