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Keywords = Maslov index

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14 pages, 268 KiB  
Article
A Construction of Maslov-Type Index for Paths of 2 × 2 Symplectic Matrices
by Yan Yang and Hai-Long Her
Mathematics 2025, 13(1), 39; https://doi.org/10.3390/math13010039 - 26 Dec 2024
Viewed by 589
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 [...] Read more.
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. Full article
(This article belongs to the Section B: Geometry and Topology)
12 pages, 288 KiB  
Article
A Maslov-Type Index in Dimension 2
by Qiyu Zhong and Hai-Long Her
Mathematics 2024, 12(14), 2281; https://doi.org/10.3390/math12142281 - 22 Jul 2024
Cited by 1 | Viewed by 848
Abstract
In this article, we define an index of the Maslov type for paths of 2×2 orthogonal symplectic matrices. The starting point is an arbitrary 2×2 orthogonal symplectic matrix rather than the identity matrix. We use this index to explain [...] Read more.
In this article, we define an index of the Maslov type for paths of 2×2 orthogonal symplectic matrices. The starting point is an arbitrary 2×2 orthogonal symplectic matrix rather than the identity matrix. We use this index to explain the geometric intersection number of a pair of Lagrangian paths and compare it with the Cappell–Lee–Miller index. Full article
(This article belongs to the Section E4: Mathematical Physics)
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