Abstract
In this paper we discuss a small nonautonomous perturbation of an autonomous system on R n which has a homoclinic solution. Regarding the small perturbation as a parameter in an appropriate space of functions we discuss various situations of co-existence of homoclinic orbits. Those conditions of various co-existence actually define bifurcation manifolds in the space of functions for linearly independent homoclinic bifurcations.
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