Proper trajectories of type {\mathbb{C}^{\ast}} of a polynomial vector field on {\mathbb{C}^2} |
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Authors: | Alvaro Bustinduy |
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Institution: | 1. Departamento de Ingenier??a Industrial, Escuela Polit??cnica Superior, Universidad Antonio de Nebrija, C/ Pirineos 55, 28040, Madrid, Spain
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Abstract: | We prove that if a polynomial vector field on ${\mathbb{C}^2}$ has a proper and non-algebraic trajectory analytically isomorphic to ${\mathbb{C}^{\ast}}$ all its trajectories are proper, and except at most one which is contained in an algebraic curve of type ${\mathbb{C}}$ all of them are of type ${\mathbb{C}^{\ast}}$ . As corollary we obtain an analytic version of Lin?CZa?denberg Theorem for polynomial foliations. |
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