Almost reducibility of linear difference systems from a spectral point of view

Álvaro Castañeda; Gonzalo Robledo

doi:10.3934/cpaa.2017097

Article Contents

2017, Volume 16, Issue 6: 1977-1988. Doi: 10.3934/cpaa.2017097

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Almost reducibility of linear difference systems from a spectral point of view

Álvaro Castañeda^, and
Gonzalo Robledo

Departamento de Matemáticas, Facultad de Ciencias, Universidad de Chile, Casilla 653, Santiago, Chile

* Corresponding author
* Corresponding author

Received: September 2016

Revised: May 2017

Published: September 2017

This research has been partially supported by MATHAMSUD program (16-MATH-04 STADE) and FONDECYT Regular 1170968

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Abstract

We prove that, under some conditions, a linear nonautonomous difference system is Bylov's almost reducible to a diagonal one whose terms are contained in the Sacker and Sell spectrum of the original system.

In the above context, we provide an example of the concept of diagonally significant system, recently introduced by Pötzsche. This example plays an essential role in the demonstration of our results.

Keywords:

Linear nonautonomous difference systems,
almost reducibility,
Sacker & Sell's spectrum,
diagonal significance,
nonautonomous hyperbolicity.

Mathematics Subject Classification: Primary: 34D09; Secondary: 37C60, 39A06.

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References

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