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

Yan Yang and Hai-Long Her ()
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Yan Yang: Department of Mathematics, Jinan University, Guangzhou 510632, China
Hai-Long Her: Department of Mathematics, Jinan University, Guangzhou 510632, China

Mathematics, 2024, vol. 13, issue 1, 1-14

Abstract: 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.

Keywords: Maslov index; Conley–Zehnder–Long index; second-order symplectic path (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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