The local Morse Homology of the critical points in the Lagrange problem
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arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866917321301295104 |
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| author | Tang, Xiuting |
| author_facet | Tang, Xiuting |
| contents | In this paper, we construct local Morse homology in a new way and compute the local Morse homology of the critical points of the Lagrange problem. As a corollary, we prove for the first time that each of the linear critical points is either a saddle point or a degenerate critical point compared to the previous conclusion that if all the linear critical points are non-degenerate, they are saddle points. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_07021 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The local Morse Homology of the critical points in the Lagrange problem Tang, Xiuting Dynamical Systems Symplectic Geometry In this paper, we construct local Morse homology in a new way and compute the local Morse homology of the critical points of the Lagrange problem. As a corollary, we prove for the first time that each of the linear critical points is either a saddle point or a degenerate critical point compared to the previous conclusion that if all the linear critical points are non-degenerate, they are saddle points. |
| title | The local Morse Homology of the critical points in the Lagrange problem |
| topic | Dynamical Systems Symplectic Geometry |
| url | https://arxiv.org/abs/2603.07021 |