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Homoclinic tangencies in $R^n$
1. | Department of Mathematics, 520 Portola Plaza, Box 951555, University of California, Los Angeles, CA 90095-1555, United States |
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].
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