Dichotomy spectrum and almost topological conjugacy on nonautonomus unbounded difference systems

Álvaro Castañeda; Gonzalo Robledo

doi:10.3934/dcds.2018094

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2018, Volume 38, Issue 5: 2287-2304. Doi: 10.3934/dcds.2018094

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Dichotomy spectrum and almost topological conjugacy on nonautonomus unbounded difference systems

Álvaro Castañeda and
Gonzalo Robledo^,

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

* Corresponding author: Gonzalo Robledo
* Corresponding author: Gonzalo Robledo

Received: August 31, 2017

Published: June 2018

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

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We construct a bijection between the solutions of a linear system of nonautonomous difference equations which is uniformly asymptotically stable and its unbounded perturbation. The key idea used to made this bijection is to consider the crossing times of the solutions with the unit sphere. This approach prompt us to introduce the concept of almost topological conjugacy in this nonautonomous framework. This task is carried out by simplifying both systems through a spectral approach of the notion of almost reducibility combined with suitable technical assumptions.

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

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