Transactions of the American Mathematical Society

Author(s): Shui-Nee Chow; Weishi Liu; Yingfei Yi
Journal: Trans. Amer. Math. Soc. 352 (2000), 5179-5211.
MSC (1991): Primary 34C30, 34C35, 34D35
Posted: June 27, 2000
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We study dynamics of flows generated by smooth vector fields in ${\mathbb{R} }^n$ in the vicinity of an invariant and closed smooth manifold

. By applying the Hadamard graph transform technique, we show that there exists an invariant manifold (called a center manifold of

) based on the information of the linearization along

, which contains every locally bounded solution and is persistent under small perturbations.

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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

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