In mathematics, Arnold's spectral sequence (also spelled Arnol'd) is a spectral sequence used in singularity theory and normal form theory as an efficient computational tool for reducing a function to canonical form near critical points. It was introduced by Vladimir Arnold in 1975.
Definition
It is a spectral sequence for the filtered de Rham complex with
The filtration coming from increasing order of poles along discriminant loci (Diagonals) E1-page has differential forms that have logarithmic singularities along the diagonals The differential encodes the relationships among the singular forms
References