Let f : M --> M denote a diffeomorphism of a smooth manifold M. Let p is an element of M be its hyperbolic fixed point with stable and unstable manifolds W-S and W-U respectively. Assume that W-S is a curve. Suppose that W-U and W-S have a degenerate homoclinic crossing at a point B not equal p, i.e., they cross at B tangentially with a finite order of contact.It is shown that, subject to C-1-linearizability and certain conditions on the invariant manifolds, a transverse homoclinic crossing will arise arbitrarily close to B. This proves the existence of a horseshoe structure arbitrarily close to B. and extends a similar planar result of Homburg and Weiss 10.
展开▼
