Oscillation theory for non-autonomous linear Hamiltonian systems

Abstract

This talk will be devoted to study oscillation properties of nonautonomous linear Hamiltonian systems applying some fundamental methods of topological dynamics and of ergodic theory. In particular, we will define and characterize the uniform weak disconjugacy concept and we will analyze the connections between disconjugacy, uniform weak disconjugacy, weak disconjugacy, and nonoscillation. A formula for the rotation number in terms of the multiplicity of the proper focal points of a conjoined basis will also be shown.