Regularizable and non-regularizable collisions in N-body problems

Regina Mart\'{\i}nez, Dept. de Matem\`atiques,
Univ. Aut\`onoma de Barcelona, Bellaterra, Barcelona, Spain

Carles Sim\'o, Dept. de Matem\`atica Aplicada i An\`alisi, 
Univ. de Barcelona, Gran Via 585, 08007 Barcelona, Spain

and 

Antoni Sus\'{\i}n, Dept. de Matem. Aplicada I, Univ. 
Polit\`ecnica de Catalunya, Diagonal 647, 08028 Barcelona, Spain

Abstract

Collisions appear as singularities in the N-body problem. A binary 
(resp. total) collision occurs when only two (resp. all) masses
collide. Between these cases other types of collisions appear, like
triple (TC), simultaneous binary (SBC), etc. We consider a geometrical
approach, searching for continuity with respect to i.c. for orbits 
passing close to a collision. After surveying known results, some 
recent progress, dealing with finite order of smoothness in the SBC 
case and with the classification of passages near TC, is presented.