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Working with a general class of linear Hamiltonian systems on $[0, 1]$, weshow that renormalized oscillation results can be obtained in a natural waythrough consideration of the Maslov index associated with appropriately chosenpaths of Lagrangian subspaces of $\mathbb{C}^{2n}$. We verify that ourapplicability class includes Dirac and Sturm-Liouville systems, as well as asystem arising from differential-algebraic equations for which the spectralparameter appears nonlinearly.

Renormalized oscillation theory for linear Hamiltonian systems on [0,1] via the Maslov index