Proceedings of the American Mathematical Society

Author(s): Ming-Chia Li
Journal: Proc. Amer. Math. Soc. 127 (1999), 289-295.
MSC (1991): Primary 58F10, 58F12, 65L20, 34D30, 34D45
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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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Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 58F10, 58F12, 65L20, 34D30, 34D45

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

DOI: 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
Copyright of article: Copyright 1999, American Mathematical Society

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