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Symplectomorphism


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.

A diffeomorphism between two symplectic manifolds is called a symplectomorphism if

where is the pullback of . The symplectic diffeomorphisms from to are a (pseudo-)group, called the symplectomorphism group (see below).


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