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A Finite-time Condition for Exponential Trichotomy in Infinite Dynamical Systems

Published online by Cambridge University Press:  20 November 2018

Arnaud Ducrot ,
Pierre Magal  and
Ousmane Seydi
Arnaud Ducrot
Affiliation:
Institut de Mathematiques de Bordeaux, Universite Bordeaux, 33000 Bordeaux, France. e-mail: arnaud.ducrot@u-bordeaux2.fr, pierre.magal@u-bordeaux2.fr, seydi86@hotmail.fr
Pierre Magal
Affiliation:
Institut de Mathematiques de Bordeaux, Universite Bordeaux, 33000 Bordeaux, France. e-mail: arnaud.ducrot@u-bordeaux2.fr, pierre.magal@u-bordeaux2.fr, seydi86@hotmail.fr
Ousmane Seydi
Affiliation:
Institut de Mathematiques de Bordeaux, Universite Bordeaux, 33000 Bordeaux, France. e-mail: arnaud.ducrot@u-bordeaux2.fr, pierre.magal@u-bordeaux2.fr, seydi86@hotmail.fr
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Abstract

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In this article we study exponential trichotomy for infinite dimensional discrete time dynamical systems. The goal of this article is to prove that finite time exponential trichotomy conditions allow us to derive exponential trichotomy for arbitrary times. We present an application to the case of pseudo orbits in some neighborhood of a normally hyperbolic set.

Keywords

34D0934A10exponential trichotomyexponential dichotomydiscrete time dynamical systemsdifference equations
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 67 , Issue 5 , 01 October 2015 , pp. 1065 - 1090
Copyright
Copyright © Canadian Mathematical Society 2014

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