A Spectral Sequence for a Graded Linear Map
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866929235005800448 |
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| author | Bates, Larry Bendersky, Martin Churchill, Richard |
| author_facet | Bates, Larry Bendersky, Martin Churchill, Richard |
| contents | We apply the method of spectral sequences to study classical problems in analysis. We illustrate the method by finding polynomial vector fields that commute with a given polynomial vector field and finding integrals of polynomial Hamiltonian systems. For the later we describe the integrals for the Henon-Heiles Hamiltonian which arises in celestial mechanics. The unifying feature is that these problems seek elements in the kernel of a linear operator. The spectral sequence approach emphasizes the obstructions constructed from cokernel of the operator to finding elements in the kernel. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2402_02560 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A Spectral Sequence for a Graded Linear Map Bates, Larry Bendersky, Martin Churchill, Richard Algebraic Topology Primary:055T99 Secondary:32M25, 37J06, 770H05 We apply the method of spectral sequences to study classical problems in analysis. We illustrate the method by finding polynomial vector fields that commute with a given polynomial vector field and finding integrals of polynomial Hamiltonian systems. For the later we describe the integrals for the Henon-Heiles Hamiltonian which arises in celestial mechanics. The unifying feature is that these problems seek elements in the kernel of a linear operator. The spectral sequence approach emphasizes the obstructions constructed from cokernel of the operator to finding elements in the kernel. |
| title | A Spectral Sequence for a Graded Linear Map |
| topic | Algebraic Topology Primary:055T99 Secondary:32M25, 37J06, 770H05 |
| url | https://arxiv.org/abs/2402.02560 |