An ergodic and topological approach to disconjugate linear Hamiltonian systems

Abstract

This paper is devoted to the qualitative study of disconjugate random linear Hamiltonian systems. We relate the principal solutions at $\pm\infty$ with the ergodic structure of the flow, the presence of exponential dichotomy, and the description of the Sacker-Sell spectrum. A continuity theorem for the principal solutions is also provided.