The well known -lemma  states the following: Let be a -diffeomorphism of with a hyperbolic fixed point at 0 and - and -dimensional stable and unstable manifolds and , respectively (). Let be a -disk in and be another p-disk in meeting at some point transversely. Then contains -disk arbitrarily -close to . In this paper we will show that the same assertion still holds outside of an arbitrarily small neighborhood of 0, even in the case of non-transverse homoclinic intersections with finite order of contact, if we assume that 0 is a low order non-resonant point.
Submitted November 4, 2002. Published April 11, 2003.
Math Subject Classifications: 37B10, 37C05, 37C15, 37D10.
Key Words: Homoclinic tangency, invariant manifolds, lambda-Lemma, order of contact, resonance
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