symplectomorphism

Etymology
.

Noun

 * 1)  An isomorphism of a symplectic manifold; a diffeomorphism which preserves symplectic structure.
 * 2) * 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 $$\textstyle F(x, y) = \int{(f dv - g du)}$$, 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.
 * 1) * 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
 * $$ \text{Sympl}(M,\omega) = \lbrace f : M \overset{\simeq}{\longrightarrow} M\ \vert\ f^*\omega= \omega \rbrace$$.
 * $$ \text{Sympl}(M,\omega) = \lbrace f : M \overset{\simeq}{\longrightarrow} M\ \vert\ f^*\omega= \omega \rbrace$$.

Translations

 * Italian: simplettomorfismo