Structural stability on basins for numerical methods
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Abstract:
In this paper, we show that a flow $\Phi$ 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).References
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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
- Received by editor(s): January 28, 1997
- Received by editor(s) in revised form: May 6, 1997
- Communicated by: Mary Rees
- © Copyright 1999 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 127 (1999), 289-295
- MSC (1991): Primary 58F10, 58F12, 65L20, 34D30, 34D45
- DOI: https://doi.org/10.1090/S0002-9939-99-04591-8
- MathSciNet review: 1469420