Symplectomorphism

English

Etymology

Template:Blend.

Noun

1. Template:Lb An isomorphism of a symplectic manifold; a diffeomorphism which preserves symplectic structure.
   • Template:Quote-book
   • 2001, A. Dzhamay, G. Wassermann (translators), V. I. Arnol'd, A. B. Givental' Symplectic Geometry, V. I. Arnol'd, S. P. Novikov (editors), Dynamical Systems IV: Symplectic Geometry and its Applications, Springer, 2nd Edition, page 39,

     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 $F(x,y)=\int (fdv-gdu)$, where $u=(X+x)/2$, $v=(Y+y)/2$, true under the assumption that the Jacobian $\partial (u,v)/\partial (x,y)$ is different from zero.

   • 2008, Ana Cannas da Silva, Lectures on Symplectic Geometry, Springer, 2nd printing with corrections, page 63,

     The symplectomorphisms of a symplectic manifold $(M,\omega )$ form the group

     $\text{Sympl}(M,\omega )=\{f:M\stackrel{\simeq }{⟶}M|f^{*}\omega =\omega \}$.

Translations

• Italian: Template:T