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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

$C^1$ Connecting Lemmas


Authors: Lan Wen and Zhihong Xia
Journal: Trans. Amer. Math. Soc. 352 (2000), 5213-5230
MSC (2000): Primary 37Cxx, 37Dxx
Published electronically: July 18, 2000
MathSciNet review: 1694382
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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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Additional Information

Lan Wen
Affiliation: Department of Mathematics, Peking University, Beijing, 100871, China
Email: lwen@math.pku.edu.cn

Zhihong Xia
Affiliation: Department of Mathematics, Northwestern University, Evanston, Illinois 60208
Email: xia@math.nwu.edu

DOI: http://dx.doi.org/10.1090/S0002-9947-00-02553-8
PII: S 0002-9947(00)02553-8
Received by editor(s): January 24, 1997
Received by editor(s) in revised form: April 13, 1998
Published electronically: July 18, 2000
Additional Notes: Both authors are supported in part by National Science Foundation and the Chinese Natural Science Foundation.
Article copyright: © Copyright 2000 American Mathematical Society