𝐶¹ Connecting Lemmas

Wen, Lan; Xia, Zhihong

doi:10.1090/S0002-9947-00-02553-8

$C^1$ Connecting Lemmas
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by Lan Wen and Zhihong Xia PDF

Trans. Amer. Math. Soc. 352 (2000), 5213-5230 Request permission

Abstract:

Like the closing lemma, the connecting lemma is of fundamental importance in dynamical systems. Hayashi recently proved the $C^1$ connecting lemma for stable and unstable manifolds of a hyperbolic invariant set. In this paper, we prove several very general $C^1$ connecting lemmas. We simplify Hayashi’s proof and extend the results to more general cases.

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