Sturm intersection theory for periodic Jacobi matrices and linear Hamiltonian systems

Abstract

Sturm–Liouville oscillation theory for periodic Jacobi operators with matrix entries is discussed and illustrated. The proof simplifies and clarifies the use of intersection theory of Bott, Maslov and Conley–Zehnder. It is shown that the eigenvalue problem for linear Hamiltonian systems can be dealt with by the same approach.