Abstract
Let γ be a hyperbolic closed orbit of a C 1 vector field X on a compact C ∞ manifold M of dimension n ≥ 3, and let H X(γ) be the homoclinic class of X containing γ. In this paper, we prove that C 1-generically, if H X(γ) is expansive and isolated, then it is hyperbolic.
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