On the Maslov and the Morse index for constrained variational problems.
An index theory is developed for symplectic differential systems. Unlike in the authors' earlier paper [Proc. Lond. Math. Soc., III. Ser. 83, 351--389 (2001; Zbl 1027.53101)], where such systems were studied in association to solutions of hyper-regular Hamiltonians, here, the case of degenerate Hamiltonians is treated via a suitable extension of the Legendre transform. Thus, a general version of the Morse index theorem for constrained variational problems is obtained.
scientific article; zbMATH DE number 1975939