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Persistence of Exponential Trichotomy for Linear Operators: A Lyapunov–Perron Approach

  • A. Ducrot
  • P. Magal
  • O. Seydi
Article

Abstract

In this article we revisit the perturbation of exponential trichotomy of linear difference equation in Banach space by using a Perron–Lyapunov fixed point formulation for the perturbed evolution operator. This approach allows us to directly re-construct the perturbed semiflow without using shift spectrum arguments. These arguments are presented to the case of linear autonomous discrete time dynamical system. This result is then coupled to Howland semigroup procedure to obtain the persistence of exponential trichotomy for non-autonomous difference equations.

Keywords

Exponential trichotomy Exponential dichotomy Discrete time dynamical systems Difference equations Howland semigroup 

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Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.Institut de Mathematiques de Bordeaux, UMR CNRS 5251Universite Bordeaux SegalenBordeauxFrance

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