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.Vladimir Arnold "Spectral sequence for reduction of functions to normal form", Funct. Anal. Appl. 9 (1975) no. 3, 81–82.Victor Goryunov, Gábor Lippner, "Simple framed curve singularities" in Majid Gazor, Pei Yu, "Spectral sequences and parametric normal forms", Journal of Differential Equations 252 (2012) no. 2, 1003–1031.
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