Singularity Theory

E1046816

branch of mathematics mathematical theory

Singularity Theory is a branch of mathematics that studies the behavior and classification of functions and spaces near points where they fail to be well-behaved, such as critical points or other types of singularities.

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Statements (72)

Predicate	Object
instanceOf	branch of mathematics ⓘ mathematical theory ⓘ
appliesTo	analytic functions ⓘ germs of functions ⓘ holomorphic mappings ⓘ polynomial mappings ⓘ smooth functions ⓘ
developedBy	Hassler Whitney NERFINISHED ⓘ Heisuke Hironaka NERFINISHED ⓘ John Milnor NERFINISHED ⓘ Oscar Zariski NERFINISHED ⓘ René Thom NERFINISHED ⓘ Vladimir Arnold NERFINISHED ⓘ
fieldOfStudy	singularities of functions ⓘ singularities of spaces ⓘ
hasApplicationArea	control theory ⓘ dynamical systems ⓘ mechanics ⓘ optics ⓘ singularities in physical models ⓘ
hasKeyResult	ADE classification of simple singularities ⓘ Morse lemma NERFINISHED ⓘ Thom’s transversality theorem NERFINISHED ⓘ Whitney stratification ⓘ classification of simple singularities ⓘ resolution of singularities in characteristic zero ⓘ
hasSubfield	equisingularity theory ⓘ singularities of algebraic varieties ⓘ singularities of complex hypersurfaces ⓘ singularities of differentiable maps ⓘ topology of singularities ⓘ
relatedTo	algebraic geometry ⓘ bifurcation theory ⓘ catastrophe theory ⓘ complex geometry ⓘ differential topology ⓘ topology ⓘ
studies	behavior of functions near singular points ⓘ bifurcations of critical points ⓘ catastrophe points ⓘ catastrophes in mappings ⓘ classification of singularities ⓘ critical points of functions ⓘ deformations of singularities ⓘ degenerate critical points ⓘ discriminant sets ⓘ equivalence classes of singularities ⓘ local behavior of algebraic varieties ⓘ local behavior of analytic maps ⓘ local behavior of complex spaces ⓘ local behavior of differentiable maps ⓘ moduli of singularities ⓘ stability of singularities ⓘ
usesConcept	Milnor number ⓘ Morse function ⓘ Morse singularity ⓘ bifurcation set ⓘ catastrophe ⓘ critical point ⓘ discriminant locus ⓘ jet space ⓘ non-Morse singularity ⓘ stable mapping ⓘ tangent cone ⓘ unfolding of a singularity ⓘ versal deformation ⓘ
usesMethod	Morse theory ⓘ algebraic geometry ⓘ commutative algebra ⓘ complex analytic geometry ⓘ differential topology NERFINISHED ⓘ stratification theory ⓘ

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Vladimir Arnold → notableWork → Singularity Theory ⓘ