Stable manifolds in the method of averaging

Author:
Stephen Schecter

Journal:
Trans. Amer. Math. Soc. **308** (1988), 159-176

MSC:
Primary 34C29; Secondary 34C30, 58F27, 58F30

MathSciNet review:
946437

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Abstract | References | Similar Articles | Additional Information

Abstract: Consider the differential equation , where is periodic in and is a small parameter, and the averaged equation . Suppose the averaged equation has a hyperbolic equilibrium at with stable manifold . Let denote the hyperbolic -periodic solution of near . We prove a result about smooth convergence of the stable manifold of to as . The proof uses ideas of Vanderbauwhede and van Gils about contractions on a scale of Banach spaces.

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Additional Information

DOI:
http://dx.doi.org/10.1090/S0002-9947-1988-0946437-2

Article copyright:
© Copyright 1988
American Mathematical Society