: Mathématiques: deformation

geometry > algebraic geometry > deformation

algebra > differential algebra > deformation

deformation

In mathematics, deformation theory is the study of infinitesimal conditions associated with varying a solution P of a problem to slightly different solutions P_ε, where ε is a small number, or a vector of small quantities. The infinitesimal conditions are the result of applying the approach of differential calculus to solving a problem with constraints. The name is an analogy to non-rigid structures that deform slightly to accommodate external forces. Some characteristic phenomena are: the derivation of first-order equations by treating the ε quantities as having negligible squares; the possibility of isolated solutions, in that varying a solution may not be possible, or does not bring anything new; and the question of whether the infinitesimal constraints actually 'integrate', so that their solution does provide small variations. In some form these considerations have a history of centuries in mathematics, but also in physics and engineering. For example, in the geometry of numbers a class of results called isolation theorems was recognised, with the topological interpretation of an open orbit (of a group action) around a given solution. Perturbation theory also looks at deformations, in general of operators.
(Wikipedia, The Free Encyclopedia, https://en.wikipedia.org/wiki/Deformation_(mathematics))

http://data.loterre.fr/ark:/67375/PSR-PK5PSW67-S

RDF/XML TURTLE JSON-LD Date de création 23/08/2023, dernière modification le 23/08/2023

Loterre