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

DOI:
https://doi.org/10.1090/S0002-9939-99-04591-8

MathSciNet review:
1469420

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Abstract | References | Similar Articles | Additional Information

Abstract: In this paper, we show that a flow 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:
https://doi.org/10.1090/S0002-9939-99-04591-8

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