Smooth roughness of exponential dichotomies, revisited

Christian Pötzsche

doi:10.3934/dcdsb.2015.20.853

Article Contents

2015, Volume 20, Issue 3: 853-859. Doi: 10.3934/dcdsb.2015.20.853

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Smooth roughness of exponential dichotomies, revisited

Christian Pötzsche^1,

1.
Institut für Mathematik, Alpen-Adria Universität Klagenfurt, Universitätsstraße 65-67, 9020 Klagenfurt

Received: September 30, 2013

Revised: March 31, 2014

Published: April 2015

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Abstract

As a direct consequence of well-established proof techniques, we establish that the invariant projectors of exponential dichotomies for parameter-dependent nonautonomous difference equations are as smooth as their right-hand sides. For instance, this guarantees that the saddle-point structure in the vicinity of hyperbolic solutions inherits its differentiability properties from the particular given equation.

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Mathematics Subject Classification: Primary: 34D09; Secondary: 37B55, 39A30.

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