| dbo:abstract |
En matemàtiques, un simplectomorfisme o mapa simplèctic és un isomorfisme en la categoria de varietats simplèctiques. En la mecànica clàssica, un simplectomorfisme representa una transformació de l'espai de fase que preserva el volum i preserva l' de l'espai de fase, i es denomina transformació canònica. (ca) Un simplectomorfismo es un difeomorfismo definido sobre una variedad simpléctica, que preserva la forma simpléctica, es decir, tal que el pullback de la forma simpléctica coincide con la propia forma simpléctica . Un difeomorfismo se llama canónico si preserva el paréntesis de Poisson definido sobre el álgebra de Poisson de la variedad, es decir: Puede probarse que todo simplectomorfismo es un difeomorfismo canónico. * Datos: Q1049064 (es) En géométrie symplectique, un symplectomorphisme est un isomorphisme de variétés symplectiques. (fr) In mathematics, a symplectomorphism or symplectic map is an isomorphism in the category of symplectic manifolds. In classical mechanics, a symplectomorphism represents a transformation of phase space that is volume-preserving and preserves the symplectic structure of phase space, and is called a canonical transformation. (en) 数学では、シンプレクティック同相(symplectomorphism)（あるいは、シンプレクティック写像(symplectic map)とも言う）は、シンプレクティック多様体のカテゴリでの同型のことを言う。古典力学では、シンプレクティック同相は、体積保存する写像で、相空間のシンプレクティック構造を保存する相空間の間の写像変換である。古典力学では正準変換と呼ばれる。 (ja) In matematica, un simplettomorfismo è un isomorfismo della categoria delle varietà simplettiche. (it) 在数学中，一个辛同胚（symplectomorphism）是辛流形范畴中的一个同构。 (zh) |
| dbo:wikiPageID |
312304 (xsd:integer) |
| dbo:wikiPageLength |
9167 (xsd:nonNegativeInteger) |
| dbo:wikiPageRevisionID |
1123241594 (xsd:integer) |
| dbo:wikiPageWikiLink |
dbr:Canonical_transformation dbr:One-parameter_group dbr:Betti_numbers dbr:Betti_number dbr:Vector_field dbr:Vladimir_Arnold dbr:Lie_derivative dbr:Lie_group dbr:Pseudogroup dbc:Hamiltonian_mechanics dbr:Critical_point_(mathematics) dbr:Mathematics dbr:Geodesics_as_Hamiltonian_flows dbr:Pullback_(differential_geometry) dbr:Classical_mechanics dbr:Energy dbr:Morse_theory dbr:Symplectic_structure dbr:Andreas_Floer dbc:Symplectic_topology dbr:Lie_algebra dbr:Liouville's_theorem_(Hamiltonian) dbr:Smooth_function dbr:Phase_space dbr:Theoretical_physics dbr:Symplectic_manifold dbr:Augustin_Banyaga dbr:Fixed_point_(mathematics) dbr:Darboux's_theorem dbr:Diffeomorphism dbr:Floer_homology dbr:Isomorphism dbr:Riemann_curvature_tensor dbr:Riemannian_manifold dbr:Hamiltonian_mechanics dbr:Hamiltonian_vector_field dbr:Hilbert_space dbr:Isometry dbr:Cotangent_bundle dbr:Simple_Lie_group dbr:Poisson_bracket dbr:Sphere dbr:Category_(mathematics) dbr:Symplectic_vector_field dbr:Hamiltonian_isotopy dbr:Pseudoholomorphic_curves dbr:Four-manifold dbr:Symplectic_form dbr:Mikhail_Gromov_(mathematician) dbr:Coadjoint_orbit dbr:Volume-preserving dbr:Homotopy_type dbr:Hofer_norm |
| dbp:wikiPageUsesTemplate |
dbt:Citation dbt:Main dbt:Math dbt:Portal dbt:Reflist dbt:See_also dbt:Short_description |
| dcterms:subject |
dbc:Hamiltonian_mechanics dbc:Symplectic_topology |
| gold:hypernym |
dbr:Isomorphism |
| rdf:type |
owl:Thing yago:WikicatConjectures yago:Abstraction100002137 yago:Cognition100023271 yago:Concept105835747 yago:Content105809192 yago:Hypothesis105888929 yago:Idea105833840 yago:PsychologicalFeature100023100 yago:Speculation105891783 |
| rdfs:comment |
En matemàtiques, un simplectomorfisme o mapa simplèctic és un isomorfisme en la categoria de varietats simplèctiques. En la mecànica clàssica, un simplectomorfisme representa una transformació de l'espai de fase que preserva el volum i preserva l' de l'espai de fase, i es denomina transformació canònica. (ca) Un simplectomorfismo es un difeomorfismo definido sobre una variedad simpléctica, que preserva la forma simpléctica, es decir, tal que el pullback de la forma simpléctica coincide con la propia forma simpléctica . Un difeomorfismo se llama canónico si preserva el paréntesis de Poisson definido sobre el álgebra de Poisson de la variedad, es decir: Puede probarse que todo simplectomorfismo es un difeomorfismo canónico. * Datos: Q1049064 (es) En géométrie symplectique, un symplectomorphisme est un isomorphisme de variétés symplectiques. (fr) In mathematics, a symplectomorphism or symplectic map is an isomorphism in the category of symplectic manifolds. In classical mechanics, a symplectomorphism represents a transformation of phase space that is volume-preserving and preserves the symplectic structure of phase space, and is called a canonical transformation. (en) 数学では、シンプレクティック同相(symplectomorphism)（あるいは、シンプレクティック写像(symplectic map)とも言う）は、シンプレクティック多様体のカテゴリでの同型のことを言う。古典力学では、シンプレクティック同相は、体積保存する写像で、相空間のシンプレクティック構造を保存する相空間の間の写像変換である。古典力学では正準変換と呼ばれる。 (ja) In matematica, un simplettomorfismo è un isomorfismo della categoria delle varietà simplettiche. (it) 在数学中，一个辛同胚（symplectomorphism）是辛流形范畴中的一个同构。 (zh) |
| rdfs:label |
Simplectomorfisme (ca) Simplectomorfismo (es) Symplectomorphisme (fr) Simplettomorfismo (it) シンプレクティック同相写像 (ja) Symplectomorphism (en) 辛同胚 (zh) |
| rdfs:seeAlso |
dbr:Phase_space_formulation |
| owl:sameAs |
freebase:Symplectomorphism wikidata:Symplectomorphism dbpedia-ca:Symplectomorphism dbpedia-es:Symplectomorphism dbpedia-fr:Symplectomorphism dbpedia-it:Symplectomorphism dbpedia-ja:Symplectomorphism dbpedia-zh:Symplectomorphism https://global.dbpedia.org/id/8BQd |
| prov:wasDerivedFrom |
wikipedia-en:Symplectomorphism?oldid=1123241594&ns=0 |
| foaf:isPrimaryTopicOf |
wikipedia-en:Symplectomorphism |
| is dbo:wikiPageRedirects of |
dbr:Arnold_conjecture dbr:Hamiltonian_symplectomorphism dbr:Symplectic_map dbr:Hamiltonian_isotopy dbr:Arnold's_conjecture dbr:Arnold_conjectures dbr:Symplectomorphic dbr:Symplectomorphisms |
| is dbo:wikiPageWikiLink of |
dbr:Canonical_coordinates dbr:Canonical_quantization dbr:Canonical_transformation dbr:List_of_differential_geometry_topics dbr:Umbral_moonshine dbr:Vladimir_Arnold dbr:Canonical_transformation_(disambiguation) dbr:Index_of_physics_articles_(S) dbr:Pseudogroup dbr:Monstrous_moonshine dbr:Conley–Zehnder_theorem dbr:Equivalent_definitions_of_mathematical_structures dbr:Lagrangian_Grassmannian dbr:Andreas_Floer dbr:Arnold_conjecture dbr:Symplectic dbr:Symplectic_group dbr:Symplectic_manifold dbr:Augustin_Banyaga dbr:Tune_shift_with_amplitude dbr:List_of_African-American_inventors_and_scientists dbr:Symplectic_category dbr:First_class_constraint dbr:Floer_homology dbr:Glossary_of_symplectic_geometry dbr:Isomorphism dbr:List_of_Greek_and_Latin_roots_in_English/P dbr:Hamiltonian_symplectomorphism dbr:Hamiltonian_mechanics dbr:Hamiltonian_vector_field dbr:Symplectic_integrator dbr:Symplectic_map dbr:Jean-Claude_Sikorav dbr:Differentiable_manifold dbr:Differential_geometry dbr:Manifold dbr:Poisson_bracket dbr:Mikhael_Gromov_(mathematician) dbr:Raphael_Douady dbr:Yakov_Eliashberg dbr:List_of_unsolved_problems_in_mathematics dbr:Thomas–Yau_conjecture dbr:Nambu_mechanics dbr:Moment_map dbr:Hamiltonian_isotopy dbr:Arnold's_conjecture dbr:Arnold_conjectures dbr:Symplectomorphic dbr:Symplectomorphisms |
| is foaf:primaryTopic of |
wikipedia-en:Symplectomorphism |
