"symplectomorphism" meaning in All languages combined

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  "etymology_text": "Blend of symplectic + isomorphism.",
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        {
          "ref": "1977, Alan Weinstein, Lectures on Symplectic Manifolds, American Mathematical Society, page 34",
          "text": "In prequantizing symplectomorphisms of the type T^*g, the only special property which we used was the fact that they preserve canonical 1-forms.",
          "type": "quotation"
        },
        {
          "text": "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,\nPoincare'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)=∫(fdv-gdu), where u=(X+x)/2, v=(Y+y)/2, true under the assumption that the Jacobian ∂(u,v)/∂(x,y) is different from zero."
        },
        {
          "text": "2008, Ana Cannas da Silva, Lectures on Symplectic Geometry, Springer, 2nd printing with corrections, page 63,\nThe symplectomorphisms of a symplectic manifold (M,ω) form the group\nSympl(M,ω)={f:M overset ≃⟶M|f^*ω=ω}."
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      "glosses": [
        "An isomorphism of a symplectic manifold; a diffeomorphism which preserves symplectic structure."
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      "id": "en-symplectomorphism-en-noun-fFzkxf32",
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        "(mathematics) An isomorphism of a symplectic manifold; a diffeomorphism which preserves symplectic structure."
      ],
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      "translations": [
        {
          "code": "it",
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          "sense": "isomorphism of a symplectic manifold",
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          "word": "simplettomorfismo"
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  "word": "symplectomorphism"
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          "text": "In prequantizing symplectomorphisms of the type T^*g, the only special property which we used was the fact that they preserve canonical 1-forms.",
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          "text": "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,\nPoincare'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)=∫(fdv-gdu), where u=(X+x)/2, v=(Y+y)/2, true under the assumption that the Jacobian ∂(u,v)/∂(x,y) is different from zero."
        },
        {
          "text": "2008, Ana Cannas da Silva, Lectures on Symplectic Geometry, Springer, 2nd printing with corrections, page 63,\nThe symplectomorphisms of a symplectic manifold (M,ω) form the group\nSympl(M,ω)={f:M overset ≃⟶M|f^*ω=ω}."
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      "code": "it",
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}