symplectomorphism
Noun
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Noun
symplectomorphism (plural symplectomorphisms)
- (mathematics) An isomorphism of a symplectic manifold; a diffeomorphism which preserves symplectic structure.
- 1977, Alan Weinstein, Lectures on Symplectic Manifolds, American Mathematical Society, page 34 ↗,
- In prequantizing symplectomorphisms of the type T*g, the only special property which we used was the fact that they preserve canonical 1-forms.
- 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.
- 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.
- 1977, Alan Weinstein, Lectures on Symplectic Manifolds, American Mathematical Society, page 34 ↗,
- Italian: simplettomorfismo
This text is extracted from the Wiktionary and it is available under the CC BY-SA 3.0 license | Terms and conditions | Privacy policy 0.002