symplectomorphism

Noun

symplectomorphism (plural symplectomorphisms)

1. An isomorphism of a symplectic manifold; a diffeomorphism which preserves symplectic structure.
   • 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...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...