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

 

Center manifolds for smooth invariant manifolds


Authors: Shui-Nee Chow, Weishi Liu and Yingfei Yi
Journal: Trans. Amer. Math. Soc. 352 (2000), 5179-5211
MSC (1991): Primary 34C30, 34C35, 34D35
Published electronically: June 27, 2000
MathSciNet review: 1650077
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Abstract:

We study dynamics of flows generated by smooth vector fields in ${\mathbb{R} }^n$ in the vicinity of an invariant and closed smooth manifold $Y$. By applying the Hadamard graph transform technique, we show that there exists an invariant manifold (called a center manifold of $Y$) based on the information of the linearization along $Y$, which contains every locally bounded solution and is persistent under small perturbations.


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Additional Information

Shui-Nee Chow
Affiliation: School of Mathematics, Georgia Institute of Technology, Atlanta, Georgia 30332-0190; Department of Mathematics, National University of Singapore, Singapore 119262
Email: chow@math.gatech.edu

Weishi Liu
Affiliation: Department of Mathematics, University of Missouri-Columbia, Columbia, Missouri 65211
Address at time of publication: Department of Mathematics, University of Kansas, Lawrence, Kansas 66045
Email: wliu@math.ukans.edu

Yingfei Yi
Affiliation: School of Mathematics, Georgia Institute of Technology, Atlanta, Georgia 30332-0190
Email: yi@math.gatech.edu

DOI: http://dx.doi.org/10.1090/S0002-9947-00-02443-0
PII: S 0002-9947(00)02443-0
Keywords: Center manifold, graph transform, overflowing
Received by editor(s): June 24, 1996
Received by editor(s) in revised form: March 20, 1998
Published electronically: June 27, 2000
Article copyright: © Copyright 2000 American Mathematical Society