Description
This thesis has been honored with the 2007 Doctorate Extraordinary Award of the Faculty of Mathematics of the University of Barcelona. We present proofs of non-integrability for some specific problems, a condition on partial integrability in a wider setting, and the use of said condition to obtain very strict upper bounds on the amount of additional first integrals for some of the aforementioned problems, including the absence of an additional integral for the Three-Body Problem.
