French
DeutschArnold's spectral sequence
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.[1][2][3]
Definition
[edit]![[icon]](/wiki/en/File:Wiki_letter_w_cropped.svg){kind=small} | This section needs expansion. You can help by adding to it. (July 2015) |
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[4]
References
[edit]- ^ 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 Geometry and Topology of Caustics. Polish Academy of Sciences. 2006. pp. 86–91.
- ^ Majid Gazor, Pei Yu, "Spectral sequences and parametric normal forms", Journal of Differential Equations 252 (2012) no. 2, 1003–1031.
- ^ Zhang, Wei. "HI-SLAM: Monocular Real-Time Dense Mapping With Hybrid Implicit Fields_supp2-3347131.mp4". doi.org. doi:10.1109/lra.2023.3347131/mm1. Retrieved 2025-07-11.
 | This algebra-related article is a stub. You can help Wikipedia by expanding it. |