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...
10 KB (1,371 words) - 22:00, 3 May 2024
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...
7 KB (1,218 words) - 22:18, 15 December 2022
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...
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or Goursat problem Darboux transformation Darboux vector Darboux's problem Darboux's theorem in symplectic geometry Darboux's theorem in real analysis,...
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Carathéodory's extension theorem, about the extension of a measure Carathéodory–Jacobi–Lie theorem, a generalization of Darboux's theorem in symplectic topology...
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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...
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Moser's trick (category Theorems in differential geometry)
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...
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having discontinuities on the interval I {\displaystyle I} . But Darboux's Theorem has an immediate consequence on the type of discontinuities that f...
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theorem (cellular automata) Cut-elimination theorem (proof theory) Dandelin's theorem (solid geometry) Danskin's theorem (convex analysis) Darboux's theorem...
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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...
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The Carathéodory–Jacobi–Lie theorem is a theorem in symplectic geometry which generalizes Darboux's theorem. Let M be a 2n-dimensional symplectic manifold...
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In mathematics, the Christoffel–Darboux formula or Christoffel–Darboux theorem is an identity for a sequence of orthogonal polynomials, introduced by Elwin...
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Nevertheless, Darboux's theorem implies that the derivative of any function satisfies the conclusion of the intermediate value theorem. Similarly to how...
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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...
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the deep connections between complex and symplectic structures. By Darboux's theorem, symplectic manifolds are isomorphic to the standard symplectic vector...
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with entries 1 and −1. Near non-regular points, the above classification theorem does not apply. However, about any point, a generalized complex manifold...
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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...
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the curvature provides a local invariant of Riemannian manifolds, Darboux's theorem states that all symplectic manifolds are locally isomorphic. The only...
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Unlike Riemannian manifolds, symplectic manifolds are not very rigid: Darboux's theorem shows that all symplectic manifolds of the same dimension are locally...
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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...
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– gives the Taylor series of the inverse of an analytic function Darboux's theorem – states that all functions that result from the differentiation of...
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study are called symplectic topology and symplectic geometry. By Darboux's theorem, a symplectic manifold has no local structure, which suggests that...
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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...
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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...
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choose coordinates so as to make the symplectic structure constant, by Darboux's theorem; and, using the associated Poisson bivector, one may consider the...
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single-variable fundamental theorem of calculus to higher dimensions, in a different vein than the generalization that is Stokes' theorem. Let G {\displaystyle...
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Integral (section Fundamental theorem of calculus)
this case, they are also called indefinite integrals. The fundamental theorem of calculus relates definite integration to differentiation and provides...
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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 )...
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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...
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Poisson manifold (section Weinstein splitting theorem)
coordinates coincides with the one described above. In general, by Darboux theorem, any arbitrary symplectic manifold ( M , ω ) {\displaystyle (M,\omega...
60 KB (9,159 words) - 20:35, 28 March 2024