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

 

Smooth robustness of exponential dichotomies


Authors: Luis Barreira and Claudia Valls
Journal: Proc. Amer. Math. Soc. 139 (2011), 999-1012
MSC (2010): Primary 34D09, 34D10, 37D99
Published electronically: July 29, 2010
MathSciNet review: 2745651
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Abstract: For sufficiently small $ C^1$-parameterized linear perturbations, we establish the robustness of exponential dichotomies in Banach spaces, with the optimal $ C^1$ dependence of the stable and unstable subspaces on the parameter.


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Additional Information

Luis Barreira
Affiliation: Departamento de Matemática, Instituto Superior Técnico, 1049-001 Lisboa, Portugal
Email: barreira@math.ist.utl.pt

Claudia Valls
Affiliation: Departamento de Matemática, Instituto Superior Técnico, 1049-001 Lisboa, Portugal
Email: cvalls@math.ist.utl.pt

DOI: http://dx.doi.org/10.1090/S0002-9939-2010-10531-2
PII: S 0002-9939(2010)10531-2
Keywords: Difference equations, parameter dependence, robustness
Received by editor(s): March 19, 2010
Received by editor(s) in revised form: March 26, 2010
Published electronically: July 29, 2010
Additional Notes: The first author was partially supported by FCT through CAMGSD, Lisbon
Communicated by: Yingfei Yi
Article copyright: © Copyright 2010 American Mathematical Society