arXiv subjects
Publications and source records attributed to Alvaro Castañeda.
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. We also provide an example of the concept of diagonally significant system, recently introduced by Pötzche. This example plays an essential role in the demonstration of our results.
We obtain sufficient conditions ensuring the topological equivalence of two perturbed difference linear systems whose linear part has a property of generalized exponential dichotomy. When the exponential dichotomy is verified, we obtain a strongly and Hölder topological equivalence.
We study differentiability properties in a particular case of the Palmer's linearization Theorem, which states the existence of an homeomorphism $H$ between the solutions of a linear ODE system having exponential dichotomy and a quasilinear system. Indeed, if the linear system is uniformly asymptotically stable, sufficient conditions ensuring that $H$ is a $C^{2}$ preserving orientation diffeomorphism are given. As an application, we generalize a converse result of density functions for a nonlinear system in the nonautonomous case.