Topological Methods in Nonlinear Analysis

Analytic invariant manifolds for nonautonomous equations

Luis Barreira and Claudia Valls

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Abstract

We construct real analytic stable invariant manifolds for sufficiently small perturbations of a linear equation $v'=A(t)v$ admitting a nonuniform exponential dichotomy. As a byproduct of our approach we obtain an exponential control not only of the trajectories on the invariant manifolds, but also of all their derivatives.

Article information

Source
Topol. Methods Nonlinear Anal., Volume 46, Number 1 (2015), 29-43.

Dates
First available in Project Euclid: 30 March 2016

Permanent link to this document
https://projecteuclid.org/euclid.tmna/1459343883

Digital Object Identifier
doi:10.12775/TMNA.2015.035

Mathematical Reviews number (MathSciNet)
MR3443676

Zentralblatt MATH identifier
1364.37068

Citation

Barreira, Luis; Valls, Claudia. Analytic invariant manifolds for nonautonomous equations. Topol. Methods Nonlinear Anal. 46 (2015), no. 1, 29--43. doi:10.12775/TMNA.2015.035. https://projecteuclid.org/euclid.tmna/1459343883


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References

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