Remote Access Proceedings of the American Mathematical Society
Green Open Access

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
DOI: https://doi.org/10.1090/S0002-9939-99-04591-8
MathSciNet review: 1469420
Full-text PDF Free Access

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).


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 58F10, 58F12, 65L20, 34D30, 34D45

Retrieve articles in all journals with MSC (1991): 58F10, 58F12, 65L20, 34D30, 34D45


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