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

 

Asymptotic behavior of stable manifolds


Author: Michal Fečkan
Journal: Proc. Amer. Math. Soc. 111 (1991), 585-593
MSC: Primary 34C29; Secondary 58F15, 58F25
MathSciNet review: 1037207
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Abstract: The relation between local stable manifolds of an ordinary differential equation and its discretization is studied. We show that a local stable manifold of a hyperbolic fixed point of an ordinary differential equation is the limit of local stable manifolds of the same fixed point of its discretizations as the discretization parameter $ h > 0$ approaches 0.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1991-1037207-3
PII: S 0002-9939(1991)1037207-3
Article copyright: © Copyright 1991 American Mathematical Society