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Center manifolds for smooth invariant manifolds
Chow, Shui-Nee Liu, Weishi Yi, Yingfei
Chow, Shui-Nee
Liu, Weishi
Yi, Yingfei
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Abstract
We study dynamics of flows generated by smooth vector fields in Rn 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.
Description
This is the published version, also available here: http://dx.doi.org/10.1090/S0002-9947-00-02443-0. First published in Trans. Amer. Math. Soc. in 2000, published by the American Mathematical Society.
Date
2000-06-27
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American Mathematical Society
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Keywords
Center manifold, graph transform, overflowing
Citation
Chow, Shui-Nee., Liu, Weishi., Yi, Yingfei. "Center manifolds for smooth invariant manifolds." Trans. Amer. Math. Soc. 352 (2000), 5179-5211. http://dx.doi.org/10.1090/S0002-9947-00-02443-0.