symplectomorphism
Sign in to saveAlso known as symplectic diffeomorphism, symplectic map
In mathematics, a symplectomorphism or symplectic map is an isomorphism in the category of symplectic manifolds. In classical mechanics, a symplectomorphism represents a transformation of phase space that is volume-preserving and preserves the symplectic structure of phase space, and is called a canonical transformation.
~6 min read
Article
7 sectionsContents
- Formal definition
- The group of (Hamiltonian) symplectomorphisms
- Comparison with Riemannian geometry
- Quantizations
- Arnold conjecture
- See also
- References
In mathematics, a symplectomorphism or symplectic map is an isomorphism in the category of symplectic manifolds. In classical mechanics, a symplectomorphism represents a transformation of phase space that is volume-preserving and preserves the symplectic structure of phase space, and is called a canonical transformation.
==Formal definition==
Connections
Mikhail Gromov
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symplectic manifold
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mathematics
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energy
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International Standard Book Number
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classical mechanics
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sphere
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digital object identifier
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theoretical physics
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bibcode
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Hilbert space
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Vladimir Arnold
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isomorphism
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vector field
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Hamiltonian mechanics
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Lie group
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fixed point
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Q22908627
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category
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isometry
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