Symplectic geometry is a branch of differential geometry and differential topology that studies symplectic manifolds; that is, differentiable manifolds...
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content of the Frobenius theorem. Contact geometry is in many ways an odd-dimensional counterpart of symplectic geometry, a structure on certain even-dimensional...
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\omega } , called the symplectic form. The study of symplectic manifolds is called symplectic geometry or symplectic topology. Symplectic manifolds arise naturally...
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properties and concepts in symplectic geometry in mathematics. The terms listed here cover the occurrences of symplectic geometry both in topology as well...
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example, in Riemannian geometry distances and angles are specified, in symplectic geometry volumes may be computed, in conformal geometry only angles are specified...
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In mathematics, a symplectic vector space is a vector space V {\displaystyle V} over a field F {\displaystyle F} (for example the real numbers R {\displaystyle...
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Maurice de Gosson: Symplectic Geometry and Quantum Mechanics (2006), p.7 and pp. 12–13 da Silva, A.C., Lectures on Symplectic Geometry, Springer (2001)...
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Vladimir Arnold (section Symplectic geometry)
systems, algebra, catastrophe theory, topology, real algebraic geometry, symplectic geometry, differential equations, classical mechanics, differential-geometric...
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In mathematics, the name symplectic group can refer to two different, but closely related, collections of mathematical groups, denoted Sp(2n, F) and Sp(n)...
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existence of exact Lagrangian immersions and similar objects in symplectic and contact geometry. His well-known book Partial Differential Relations collects...
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manifold Symplectic topology Symplectic space Symplectic manifold Symplectic structure Symplectomorphism Contact structure Contact geometry Hamiltonian...
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refer to: Symplectic category Symplectic Clifford algebra, see Weyl algebra Symplectic geometry Symplectic group, and corresponding symplectic Lie algebra...
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momentum coordinates is available in the mathematical setting of symplectic geometry. Liouville's theorem ignores the possibility of chemical reactions...
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A symplectic space may refer to: Symplectic manifold Symplectic vector space This disambiguation page lists articles associated with the title Symplectic...
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Poisson manifold (redirect from Symplectic leaf)
symplectic form ω {\displaystyle \omega } , but satisfies the same algebraic properties. Poisson geometry is closely related to symplectic geometry:...
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is a British mathematician who deals with symplectic manifolds and their interaction with algebraic geometry, low-dimensional topology, and dynamics. He...
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Momentum map (redirect from Symplectic quotient)
In mathematics, specifically in symplectic geometry, the momentum map (or, by false etymology, moment map) is a tool associated with a Hamiltonian action...
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mathematics, a symplectic vector field is one whose flow preserves a symplectic form. That is, if ( M , ω ) {\displaystyle (M,\omega )} is a symplectic manifold...
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Non-squeezing theorem (redirect from Symplectic capacity)
symplectic geometry. It was first proven in 1985 by Mikhail Gromov. The theorem states that one cannot embed a ball into a cylinder via a symplectic map...
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Ruppeiner geometry Solid geometry Spherical geometry Symplectic geometry Synthetic geometry Systolic geometry Taxicab geometry Toric geometry Transformation...
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1959) is a Japanese mathematician known for his work in symplectic geometry and Riemannian geometry. His many fundamental contributions to mathematics include...
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phenomena. Hamiltonian mechanics has a close relationship with geometry (notably, symplectic geometry and Poisson structures) and serves as a link between classical...
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theorems: Gromov's compactness theorem (geometry) in Riemannian geometry Gromov's compactness theorem (topology) in symplectic topology Gromov's Betti number theorem [ru]...
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complex geometry leading to the Borel–Weil–Bott theorem, or in symplectic geometry, where Kähler manifolds are symplectic, in Riemannian geometry where...
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Arnold conjecture (category Symplectic geometry)
symplectic geometry, a branch of differential geometry. Let ( M , ω ) {\displaystyle (M,\omega )} be a closed (compact without boundary) symplectic manifold...
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cover many areas in differential geometry and mathematical physics, including Riemannian geometry, symplectic geometry, Lie groupoids, geometric mechanics...
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particularly in representation theory, a symplectic resolution is a morphism that combines symplectic geometry and resolution of singularities. Let π :...
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In mathematics, a symplectic matrix is a 2 n × 2 n {\displaystyle 2n\times 2n} matrix M {\displaystyle M} with real entries that satisfies the condition...
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Gromov–Witten invariant (category Symplectic topology)
In mathematics, specifically in symplectic topology and algebraic geometry, Gromov–Witten (GW) invariants are rational numbers that, in certain situations...
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Darboux's theorem (category Symplectic geometry)
fields, the chief among them being symplectic geometry. Indeed, one of its many consequences is that any two symplectic manifolds of the same dimension are...
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