A Spectral Sequence for a Graded Linear Map
Algebraic Topology
2024-02-07 v1
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.
Cite
@article{arxiv.2402.02560,
title = {A Spectral Sequence for a Graded Linear Map},
author = {Larry Bates and Martin Bendersky and Richard Churchill},
journal= {arXiv preprint arXiv:2402.02560},
year = {2024}
}