abstr3
A theorem on the dependence of Poincaré mappings for different
functional differential equations (FDEs) on the right hand side of the equation is proved.
Together with recent results on hyperbolic sets for noninvertible mappings,
this is used to describe how Poincaré mappings and their complicated behavior in the
neighborhood of a transversal homoclinic orbit persist under FDE perturbations of the equation.
The method is shown to apply to three example equations, where Poincaré mappings with such behavior
are known to exist.