symplectomorphism

plural symplectomorphisms

1. mathematicsAn 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}.

   2 more examples

   In prequantizing symplectomorphisms of the type T^*g, the only special property which we used was the fact that they preserve canonical 1-forms.

   1977, Alan Weinstein, Lectures on Symplectic Manifolds, American Mathematical Society, page 34

   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.

   2001, V. I. Arnol'd, A. B. Givental', “Symplectic Geometry”, in A. Dzhamay, G. Wassermann, transl., edited by V. I. Arnol'd and S. P. Novikov, Dynamical Systems IV: Symplectic Geometry and its Applications, 2nd edition, Springer, page 39