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Pronunciation varies by accent · noun
(mathematics) An isomorphism of a symplectic manifold; a diffeomorphism which preserves symplectic structure..
2008, Ana Cannas da Silva, Lectures on Symplectic Geometry, Springer, 2nd printing with corrections, page 63, The symplectomorphisms of a symplectic manifold (M,ω) form the group Sympl(M,ω)={f:M overset ≃⟶M|f^*ω=ω}.
In prequantizing symplectomorphisms of the type T^*g, the only special property which we used was the fact that they preserve canonical 1-forms.
Poincare's argument is based on the fact that the fixed points of a symplectomorphism of the annulus are precisely the critical points of the function #92;textstyleF(x,y)#61;#92;int#123;(fdv-gdu)#125;, where u#61;(X#43;x)#47;2, v#61;(Y#43;y)#47;2, true under the assumption that the Jacobian #92;partial(u,v)#47;#92;partial(x,y) is different from zero.
Use symplectomorphism when its meaning, tone and grammar fit the full sentence. A synonym is not always a direct replacement.
Symplectomorphism means (mathematics) An isomorphism of a symplectic manifold; a diffeomorphism which preserves symplectic structure..
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2008, Ana Cannas da Silva, Lectures on Symplectic Geometry, Springer, 2nd printing with corrections, page 63, The symplectomorphisms of a symplectic manifold (M,ω) form the group Sympl(M,ω)={f:M overset ≃⟶M|f^*ω=ω}.
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