Abstract
This paper establishes the existence and analyticity of homoclinic loop bifurcation surfaces H \mathcal {H} and multiplicity-two, limit cycle bifurcation surfaces C \mathcal {C} for planar systems depending on two or more parameters; it determines the side of H \mathcal {H} or C \mathcal {C} on which limit cycles occur; and it shows that if H \mathcal {H} and C \mathcal {C} intersect, then typically they do so at a flat contact.
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