Abstract
There exists a two-parameter family of orientation-reversing two-dimensional conservative and dissipative maps in which the stable and unstable manifolds intersect transversely from their birth and they do not experience the first direct tangency in the course of the change of parameter. We discuss the reason why the first direct tangency is inhibited in such systems. Numerical examples are given. Finally three theorems on the non-existence of the first direct heteroclinic tangency are given.
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