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...

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

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...

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

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

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...

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}...

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

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...

analysis) Darboux's theorem (real analysis) Denjoy–Carleman theorem (functional analysis) Denjoy-Young-Saks theorem (real analysis) Dini's theorem (analysis)...

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...

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

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...

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

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...

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

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 non-squeezing theorem, also called Gromov's non-squeezing theorem, is one of the most important theorems in symplectic geometry. It was first proven...

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

the dimension of a symplectic vector space is even if it is finite. Darboux theorem Symplectic frame bundle Symplectic spinor bundle Symplectic vector...

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

induces a pairing of odd and even variables. There is a version of the Darboux theorem for P-manifolds, which allows one to equip a P-manifold locally with...

differentiable. ATS theorem Carleson's theorem Dirichlet kernel Discrete Fourier transform Fast Fourier transform Fejér's theorem Fourier analysis Fourier...

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 mathematical field of analysis, a well-known theorem describes the set of discontinuities of a monotone real-valued function of a real variable;...

– 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...

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 the...