In
mathematics, Arnold's spectral sequence (also spelled Arnol'd) is a
spectral sequence
In homological algebra and algebraic topology, a spectral sequence is a means of computing homology groups by taking successive approximations. Spectral sequences are a generalization of exact sequences, and since their introduction by , they hav ...
used in
singularity theory
In mathematics, singularity theory studies spaces that are almost manifolds, but not quite. A string can serve as an example of a one-dimensional manifold, if one neglects its thickness. A singularity can be made by balling it up, dropping it ...
and
normal form theory as an efficient computational tool for reducing a
function to
canonical form
In mathematics and computer science, a canonical, normal, or standard form of a mathematical object is a standard way of presenting that object as a mathematical expression. Often, it is one which provides the simplest representation of an ob ...
near
critical points. It was introduced by
Vladimir Arnold
Vladimir Igorevich Arnold (alternative spelling Arnol'd, russian: link=no, Влади́мир И́горевич Арно́льд, 12 June 1937 – 3 June 2010) was a Soviet and Russian mathematician. While he is best known for the Kolmogorov– ...
in 1975.
[Majid Gazor, Pei Yu,]
Spectral sequences and parametric normal forms
, ''Journal of Differential Equations'' 252 (2012) no. 2, 1003–1031.
Definition
References
{{Algebra-stub
Spectral sequences
Singularity theory