Iteration formulae of the Maslov-type index theory in weak symplectic Hilbert spaces

TL;DR

This paper develops new iteration formulae for Maslov-type indices in weak symplectic Hilbert spaces, providing a splitting formula and a direct proof, advancing the mathematical understanding of symplectic path indices.

Contribution

It introduces novel iteration formulae and a splitting formula for Maslov-type indices in weak symplectic Hilbert spaces, with direct proofs enhancing theoretical foundations.

Findings

Established a splitting formula for Maslov-type indices

Derived iteration formulae for symplectic paths

Provided direct proofs for the formulae

Abstract

In this paper, we prove a splitting formula for the Maslov-type indices of symplectic paths induced by the splitting of the nullity in weak symplectic Hilbert space. Then we give a direct proof of iteration formulae for the Maslov-type indices of symplectic paths.