Abstract
We study manifolds describing the behavior of motions close to the origin and at infinity of configuration space, for mechanical systems with homogeneous potentials. We find an inversion between these behaviors when the sign of the degree of homogeneity is changed. In some cases, the blow up equations can be written in canonical form, by first reducing to a contact structure. A motivation for the use of blow-up techniques is given, and some examples are studied in detail.
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