Asymptotic behavior of stable manifolds

Fečkan, Michal

doi:10.1090/S0002-9939-1991-1037207-3

Asymptotic behavior of stable manifolds
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by Michal Fečkan

Proc. Amer. Math. Soc. 111 (1991), 585-593

DOI: https://doi.org/10.1090/S0002-9939-1991-1037207-3

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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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