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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Structural stability on basins
for numerical methods


Author: Ming-Chia Li
Journal: Proc. Amer. Math. Soc. 127 (1999), 289-295
MSC (1991): Primary 58F10, 58F12, 65L20, 34D30, 34D45
MathSciNet review: 1469420
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Abstract | References | Similar Articles | Additional Information

Abstract: In this paper, we show that a flow $\varphi $ with a hyperbolic compact attracting set is structurally stable on the basin of attraction with respect to numerical methods. The result is a generalized version of earlier results by Garay, Li, Pugh, and Shub. The proof relies heavily on the usual invariant manifold theory elaborated by Hirsch, Pugh, and Shub (1977), and by Robinson (1976).


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Additional Information

Ming-Chia Li
Affiliation: Department of Mathematics, National Changhua University of Education, Changhua 500, Taiwan
Email: mcli@math.ncue.edu.tw

DOI: http://dx.doi.org/10.1090/S0002-9939-99-04591-8
PII: S 0002-9939(99)04591-8
Keywords: Structural stability, dynamical systems, hyperbolic attracting set, basin of attraction, numerical method, Euler's method
Received by editor(s): January 28, 1997
Received by editor(s) in revised form: May 6, 1997
Communicated by: Mary Rees
Article copyright: © Copyright 1999 American Mathematical Society