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1 个结果
  • 简介:LetXdenoteacomplexanalyticmanifold,andletAut(X)denotethespaceofinvertiblemapsofagerm(X,a)toagerm(X,b);thisspaceisobviouslyagroupoid;roughlyspeaking,a'Liegroupoid'isasubgroupoidofAut(X)definedbyasystemofpartialdifferentialequations.ToafoliationwithsingularitiesonXoneattachessuchagroupoid,e.g.thesmallestonewhoseLiealgebracontainsthevectorfieldstangenttothefoliation.Itiscalled'theGaloisgroupoidofthefoliation'.Someexamplesareconsidered,forinstancefoliationsofcodimensionone,andfoliationsdefinedbylineardifferentialequations;inthislastcaseonerecuperatestheusualdifferentialGaloisgroup.

  • 标签: 非线性微分方程 微分Galois群 复解析流形 包络 Lie广群 LIE对称