See symplectomorphism in All languages combined, or Wiktionary
{ "etymology_templates": [ { "args": { "1": "en", "2": "symplectic", "3": "isomorphism" }, "expansion": "Blend of symplectic + isomorphism", "name": "blend" } ], "etymology_text": "Blend of symplectic + isomorphism.", "forms": [ { "form": "symplectomorphisms", "tags": [ "plural" ] } ], "head_templates": [ { "args": {}, "expansion": "symplectomorphism (plural symplectomorphisms)", "name": "en-noun" } ], "lang": "English", "lang_code": "en", "pos": "noun", "senses": [ { "categories": [ { "kind": "other", "name": "English blends", "parents": [], "source": "w" }, { "kind": "other", "name": "English entries with incorrect language header", "parents": [ "Entries with incorrect language header", "Entry maintenance" ], "source": "w" }, { "kind": "other", "name": "Entries with translation boxes", "parents": [], "source": "w" }, { "kind": "other", "name": "Pages with 1 entry", "parents": [], "source": "w" }, { "kind": "other", "name": "Pages with entries", "parents": [], "source": "w" }, { "kind": "other", "name": "Terms with Italian translations", "parents": [], "source": "w" }, { "kind": "topical", "langcode": "en", "name": "Mathematics", "orig": "en:Mathematics", "parents": [ "Formal sciences", "Sciences", "All topics", "Fundamental" ], "source": "w" } ], "examples": [ { "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": "quote" }, { "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}." } ], "glosses": [ "An isomorphism of a symplectic manifold; a diffeomorphism which preserves symplectic structure." ], "id": "en-symplectomorphism-en-noun-fFzkxf32", "links": [ [ "mathematics", "mathematics" ], [ "isomorphism", "isomorphism" ], [ "symplectic", "symplectic" ], [ "manifold", "manifold" ], [ "diffeomorphism", "diffeomorphism" ] ], "raw_glosses": [ "(mathematics) An isomorphism of a symplectic manifold; a diffeomorphism which preserves symplectic structure." ], "topics": [ "mathematics", "sciences" ], "translations": [ { "code": "it", "lang": "Italian", "sense": "isomorphism of a symplectic manifold", "tags": [ "masculine" ], "word": "simplettomorfismo" } ], "wikipedia": [ "symplectomorphism" ] } ], "word": "symplectomorphism" }
{ "etymology_templates": [ { "args": { "1": "en", "2": "symplectic", "3": "isomorphism" }, "expansion": "Blend of symplectic + isomorphism", "name": "blend" } ], "etymology_text": "Blend of symplectic + isomorphism.", "forms": [ { "form": "symplectomorphisms", "tags": [ "plural" ] } ], "head_templates": [ { "args": {}, "expansion": "symplectomorphism (plural symplectomorphisms)", "name": "en-noun" } ], "lang": "English", "lang_code": "en", "pos": "noun", "senses": [ { "categories": [ "English blends", "English countable nouns", "English entries with incorrect language header", "English lemmas", "English nouns", "English terms with quotations", "Entries with translation boxes", "Pages with 1 entry", "Pages with entries", "Terms with Italian translations", "en:Mathematics" ], "examples": [ { "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": "quote" }, { "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}." } ], "glosses": [ "An isomorphism of a symplectic manifold; a diffeomorphism which preserves symplectic structure." ], "links": [ [ "mathematics", "mathematics" ], [ "isomorphism", "isomorphism" ], [ "symplectic", "symplectic" ], [ "manifold", "manifold" ], [ "diffeomorphism", "diffeomorphism" ] ], "raw_glosses": [ "(mathematics) An isomorphism of a symplectic manifold; a diffeomorphism which preserves symplectic structure." ], "topics": [ "mathematics", "sciences" ], "wikipedia": [ "symplectomorphism" ] } ], "translations": [ { "code": "it", "lang": "Italian", "sense": "isomorphism of a symplectic manifold", "tags": [ "masculine" ], "word": "simplettomorfismo" } ], "word": "symplectomorphism" }
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This page is a part of the kaikki.org machine-readable English dictionary. This dictionary is based on structured data extracted on 2024-12-21 from the enwiktionary dump dated 2024-12-04 using wiktextract (d8cb2f3 and 4e554ae). The data shown on this site has been post-processed and various details (e.g., extra categories) removed, some information disambiguated, and additional data merged from other sources. See the raw data download page for the unprocessed wiktextract data.
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