2024/02/04 by Bates, Larry, Bendersky, Martin, Churchill, Richard
#37J06 #770H05 #Algebraic Topology (math.AT) #FOS: Mathematics #Primary:055T99 Secondary:32M25
paper · doi:10.48550/arxiv.2402.02560
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.