Invariant Unstable Manifolds of Nonautonomous Systems on Time Scales

Abstract

This paper is concerned with the existence of invariant manifolds for dynamical equations on a periodic time scale when the nonlinear perturbation has a small global Lipschitz constant. Particularly, for time-varying non-regressive dynamical equations, which have exponential dichotomies on a periodic time scale with bounded graininess, we use the method of graph transforms as in [1] to prove that there exists a unique integral manifold of that systems.