A Construction of Maslov-Type Index for Paths of 2 × 2 Symplectic Matrices

In this article, we construct a kind of Maslov-type index for general paths of 2×2 symplectic matrices that have two arbitrary endpoints. Our method is consistent and direct no matter whether the starting point of the path is an identity or not, which is different from those regarding the Conley–Zehnder–Long index of symplectic paths starting from an identity and Long’s Maslov-type index of symplectic path segments. In addition, we compare this index with the Conley–Zehnder–Long index.