Some Properties of the Angles between Lineals of Solutions of Exponentially Dichotomous Systems

Abstract

We prove that the maximum angle between two arbitrary unstable solution subspaces of an exponentially dichotomous finite-dimensional system on the half-line tends to zero as the time variable tends to infinity. In particular, there exists a positive constant such that the angle between an arbitrary unstable solution subspace and the stable lineal of the system is greater than this constant for all sufficiently large times.