In differential geometry, a field in mathematics, Darboux's theorem is a theorem providing a normal form for special classes of differential 1-forms, partially...

In mathematics, Darboux's theorem is a theorem in real analysis, named after Jean Gaston Darboux. It states that every function that results from the differentiation...

or Goursat problem Darboux transformation Darboux vector Darboux's problem Darboux's theorem in symplectic geometry Darboux's theorem in real analysis,...

the classical Darboux's theorem. They were proved by Alan Weinstein in 1971. This statement is a direct generalisation of Darboux's theorem, which is recovered...

Carathéodory's extension theorem, about the extension of a measure Carathéodory–Jacobi–Lie theorem, a generalization of Darboux's theorem in symplectic topology...

complicated example is given by the Conway base 13 function. In fact, Darboux's theorem states that all functions that result from the differentiation of...

F'(x)=f(x)} for every x ∈ I {\displaystyle x\in I} . According to Darboux's theorem, the derivative function f : I → R {\displaystyle f:I\to \mathbb {R}...

standard argument for the modern proof of Darboux's theorem, as well as for the proof of Darboux-Weinstein theorem and other normal form results. Let { ω...

theorem (cellular automata) Cut-elimination theorem (proof theory) Dandelin's theorem (solid geometry) Danskin's theorem (convex analysis) Darboux's theorem...

partial results such as Darboux's theorem and the Cartan-Kähler theorem. Despite being named for Ferdinand Georg Frobenius, the theorem was first proven by...

The Carathéodory–Jacobi–Lie theorem is a theorem in symplectic geometry which generalizes Darboux's theorem. Let M be a 2n-dimensional symplectic manifold...

the deep connections between complex and symplectic structures. By Darboux's theorem, symplectic manifolds are isomorphic to the standard symplectic vector...

Nevertheless, Darboux's theorem implies that the derivative of any function satisfies the conclusion of the intermediate value theorem. Similarly to how...

x_{0}} . f ′ {\displaystyle \displaystyle f'} does not skip values (by Darboux's theorem), so it has to be zero at some point between the positive and negative...

a c between a and b such that f(c) = y. This is a consequence of Darboux's theorem. The set of discontinuities of f must be a meagre set. This set must...

In mathematics, the Christoffel–Darboux formula or Christoffel–Darboux theorem is an identity for a sequence of orthogonal polynomials, introduced by Elwin...

the curvature provides a local invariant of Riemannian manifolds, Darboux's theorem states that all symplectic manifolds are locally isomorphic. The only...

with entries 1 and −1. Near non-regular points, the above classification theorem does not apply. However, about any point, a generalized complex manifold...

Unlike Riemannian manifolds, symplectic manifolds are not very rigid: Darboux's theorem shows that all symplectic manifolds of the same dimension are locally...

choose coordinates so as to make the symplectic structure constant, by Darboux's theorem; and, using the associated Poisson bivector, one may consider the...

following: As a closed nondegenerate symplectic 2-form ω. According to the Darboux's theorem, in a small neighbourhood around any point on M there exist suitable...

– gives the Taylor series of the inverse of an analytic function Darboux's theorem – states that all functions that result from the differentiation of...

even-dimensional we can take local coordinates (p1,...,pn, q1,...,qn), and by Darboux's theorem the symplectic form ω can be, at least locally, written as ω = ∑ dpk...

this case, they are also called indefinite integrals. The fundamental theorem of calculus relates definite integration to differentiation and provides...

space curves, the Darboux vector is the angular velocity vector of the Frenet frame of a space curve. It is named after Gaston Darboux who discovered it...

single-variable fundamental theorem of calculus to higher dimensions, in a different vein than the generalization that is Stokes' theorem. Let G {\displaystyle...

study are called symplectic topology and symplectic geometry. By Darboux's theorem, a symplectic manifold has no local structure, which suggests that...

as Gauss's flux theorem (or sometimes Gauss's theorem), is one of Maxwell's equations. It is an application of the divergence theorem, and it relates...

any fibre inherits the structure of a symplectic vector space. By Darboux's theorem, the constant rank embedding is locally determined by i ∗ ( T M )...

In the differential geometry of surfaces, a Darboux frame is a natural moving frame constructed on a surface. It is the analog of the Frenet–Serret frame...