Differentiability with respect to parameters in global smooth linearization

Rodrigues, Hildebrando M.; Solà-Morales, J.

doi:10.1016/j.jde.2016.11.038

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Cited by 4 publications

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“…Recently, weaker conditions for C 1 linearization were obtained in [34,35] in R 2 and in [36] in Banach spaces. Differentiable depedence on parameters was discussed in [26].…”

Section: Introductionmentioning

confidence: 99%

Smooth linearization of nonautonomous difference equations with a nonuniform dichotomy

Dragičević

Zhang

2018

Math. Z.

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In this paper we give a smooth linearization theorem for nonautonomous difference equations with a nonuniform strong exponential dichotomy. The linear part of such a nonautonomous difference equation is defined by a sequence of invertible linear operators on R d . Reducing the linear part to a bounded linear operator on a Banach space, we discuss the spectrum and its spectral gaps. Then we obtain a gap condition for C 1 linearization of such a nonautonomous difference equation. .Our theorems improve known results even in the case of uniform strong exponential dichotomies.

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“…Recently, weaker conditions for C 1 linearization were obtained in [34,35] in R 2 and in [36] in Banach spaces. Differentiable depedence on parameters was discussed in [26].…”

Section: Introductionmentioning

confidence: 99%