The transversal homoclinic points are dense in the codimension-1 Hénon-like strange attractors

Cao, Yongluo

doi:10.1090/S0002-9939-99-04787-5

The transversal homoclinic points are dense in the codimension-$1$ Hénon-like strange attractors
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Proc. Amer. Math. Soc. 127 (1999), 1877-1883 Request permission

Abstract:

We consider the codimension-1 Hénon-like strange attractors $\Lambda$. We prove that the transversal homoclinic points are dense in $\Lambda$, and that hyperbolic periodic points are dense in $\Lambda$. Moreover the hyperbolic periodic points that are heteroclinically related to the primary fixed point ( transversal intersection of stable and unstable manifolds) are dense in $\Lambda$.

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