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arXiv · 2402.02560

A Spectral Sequence for a Graded Linear Map

Larry Bates·Martin Bendersky·Richard Churchill
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Abstract

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.

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Larry Bates, Martin Bendersky, Richard Churchill. 2024-02-04. A Spectral Sequence for a Graded Linear Map. https://arxiv.org/abs/2402.02560

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