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 <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>2</mn><mo>×</mo><mn>2</mn></mrow>...
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2024-12-01
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| author | Yan Yang Hai-Long Her |
| author_facet | Yan Yang Hai-Long Her |
| author_sort | Yan Yang |
| collection | DOAJ |
| description | In this article, we construct a kind of Maslov-type index for general paths of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>2</mn><mo>×</mo><mn>2</mn></mrow></semantics></math></inline-formula> 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. |
| format | Article |
| id | doaj-art-8778d18882f14103be648e631dc3a792 |
| institution | Kabale University |
| issn | 2227-7390 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | MDPI AG |
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| series | Mathematics |
| spelling | doaj-art-8778d18882f14103be648e631dc3a7922025-01-10T13:18:03ZengMDPI AGMathematics2227-73902024-12-011313910.3390/math13010039A Construction of Maslov-Type Index for Paths of 2 × 2 Symplectic MatricesYan Yang0Hai-Long Her1Department of Mathematics, Jinan University, Guangzhou 510632, ChinaDepartment of Mathematics, Jinan University, Guangzhou 510632, ChinaIn this article, we construct a kind of Maslov-type index for general paths of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>2</mn><mo>×</mo><mn>2</mn></mrow></semantics></math></inline-formula> 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.https://www.mdpi.com/2227-7390/13/1/39Maslov indexConley–Zehnder–Long indexsecond-order symplectic path |
| spellingShingle | Yan Yang Hai-Long Her A Construction of Maslov-Type Index for Paths of 2 × 2 Symplectic Matrices Mathematics Maslov index Conley–Zehnder–Long index second-order symplectic path |
| title | A Construction of Maslov-Type Index for Paths of 2 × 2 Symplectic Matrices |
| title_full | A Construction of Maslov-Type Index for Paths of 2 × 2 Symplectic Matrices |
| title_fullStr | A Construction of Maslov-Type Index for Paths of 2 × 2 Symplectic Matrices |
| title_full_unstemmed | A Construction of Maslov-Type Index for Paths of 2 × 2 Symplectic Matrices |
| title_short | A Construction of Maslov-Type Index for Paths of 2 × 2 Symplectic Matrices |
| title_sort | construction of maslov type index for paths of 2 2 symplectic matrices |
| topic | Maslov index Conley–Zehnder–Long index second-order symplectic path |
| url | https://www.mdpi.com/2227-7390/13/1/39 |
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