A Maslov-type index theory for symplectic paths (Q1386865)

The theory of the Maslov-type index for nondegenerate continuous paths starting from the identity matrix in the symplectic group \(\text{Sp}(2n)\) was established in the paper [\textit{C. Conley} and \textit{E. Zehnder}, Commun. Pure Appl. Math. 37, 207-253 (1984; Zbl 0559.58019)], in the case \(n\geq 2\) and in [\textit{Y. Long} and \textit{E. Zehnder}, ``Morse theory for forced oscillations of asymptotically linear Hamiltonian systems'', Stochastic Processes, Physics and Geometry, Ascona 1988, 528-563 (1990)], in the case \(n=1\). Later it was extended to the case of degenerate paths which are fundamental solutions of linear Hamiltonian systems with periodic coefficients in [\textit{Y. Long}, Sci. China, Ser. A 33, 1409-1419 (1990; Zbl 0736.58022)], and, independently, in [\textit{C. Viterbo}, Invent. Math. 100, 301-320 (1990; Zbl 0727.58015)]. The present paper extends the above mentioned indices to the case of all continuous paths in \(\text{ Sp}(2n)\). The obtained index is uniquely characterized by a set of axioms.