symplectomorphism
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Symplectomorphism — In mathematics, a symplectomorphism is an isomorphism in the category of symplectic manifolds. Formal definitionSpecifically, let ( M 1, omega;1) and ( M 2, omega;2) be symplectic manifolds. A map : f : M 1 rarr; M 2 is a symplectomorphism if it… … Wikipedia
Floer homology — is a mathematical tool used in the study of symplectic geometry and low dimensional topology. First introduced by Andreas Floer in his proof of the Arnold conjecture in symplectic geometry, Floer homology is a novel homology theory arising as an… … Wikipedia
Hamiltonian mechanics — is a re formulation of classical mechanics that was introduced in 1833 by Irish mathematician William Rowan Hamilton. It arose from Lagrangian mechanics, a previous re formulation of classical mechanics introduced by Joseph Louis Lagrange in 1788 … Wikipedia
Canonical transformation — In Hamiltonian mechanics, a canonical transformation is a change of canonical coordinates (mathbf{q}, mathbf{p}, t) ightarrow (mathbf{Q}, mathbf{P}, t) that preserves the form of Hamilton s equations, although it might not preserve the… … Wikipedia
Symplectic manifold — In mathematics, a symplectic manifold is a smooth manifold, M, equipped with a closed nondegenerate differential 2 form, ω, called the symplectic form. The study of symplectic manifolds is called symplectic geometry or symplectic topology.… … Wikipedia
Canonical quantization — In physics, canonical quantization is one of many procedures for quantizing a classical theory. Historically, this was the earliest method to be used to build quantum mechanics. When applied to a classical field theory it is also called second… … Wikipedia
Differential geometry — A triangle immersed in a saddle shape plane (a hyperbolic paraboloid), as well as two diverging ultraparallel lines. Differential geometry is a mathematical discipline that uses the techniques of differential and integral calculus, as well as… … Wikipedia
Canonical coordinates — In mathematics and classical mechanics, canonical coordinates are particular sets of coordinates on the phase space, or equivalently, on the cotangent manifold of a manifold. Canonical coordinates arise naturally in physics in the study of… … Wikipedia
Vladimir Arnold — Vladimir Igorevich Arnol d or Arnold ( ru. Владимир Игоревич Арнольд, born June 12, 1937 in Odessa, Ukrainian SSR) is a Russian mathematician. While he is best known for the Kolmogorov Arnold Moser theorem regarding the stability of integrable… … Wikipedia
Poisson bracket — In mathematics and classical mechanics, the Poisson bracket is an important operator in Hamiltonian mechanics, playing a central role in the definition of the time evolution of a dynamical system in the Hamiltonian formulation. In a more general… … Wikipedia
