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| Martelo,Mitchael; Scárdua,Bruno. |
| In this note we announce some results in the study of groups of formal or germs of analytic diffeomorphisms in several complex variables. Such groups are related to the study of the transverse structure and dynamics of Holomorphic foliations, via the holonomy group notion of a foliation's leaf. For dimension one, there is a well-established dictionary relating analytic/formal classification of the group, with its algebraic properties (finiteness, commutativity, solvability, among others). Such system of equivalences also characterizes the existence of suitable integrating factors, i.e., invariant vector fields and one-forms associated to the group. Our aim is to state the basic lines of such dictionary for the case of several complex variables groups. Our... |
| Tipo: Info:eu-repo/semantics/article |
Palavras-chave: Formal complex diffeomorphism; Infinitesimal generator; Holomorphic foliation; Germ of complex diffeomorphism. |
| Ano: 2012 |
URL: http://www.scielo.br/scielo.php?script=sci_arttext&pid=S0001-37652012000400002 |
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| MOVASATI,HOSSEIN. |
| Let <img ALIGN="BOTTOM" src="http:/img/fbpe/aabc/v73n2/m4img1.gif"> be a foliation in the projective space of dimension two with a first integral of the type <img ALIGN="MIDDLE" src="http:/img/fbpe/aabc/v73n2/m4img2.gif">, where F and G are two polynomials on an affine coordinate, <img ALIGN="MIDDLE" src="http:/img/fbpe/aabc/v73n2/m4img3.gif"> = <img ALIGN="MIDDLE" src="http:/img/fbpe/aabc/v73n2/m4img4.gif"> and g.c.d.(p, q) = 1. Let z be a nondegenerate critical point of <img ALIGN="MIDDLE" src="http:/img/fbpe/aabc/v73n2/m4img2.gif">, which is a center singularity of <img ALIGN="BOTTOM" src="http:/img/fbpe/aabc/v73n2/m4img1.gif">, and <img src="http:/img/fbpe/aabc/v73n2/ft.gif" alt="ft.gif (149 bytes)"... |
| Tipo: Info:eu-repo/semantics/article |
Palavras-chave: Holomorphic foliation; Limit cycle; Center singularity. |
| Ano: 2001 |
URL: http://www.scielo.br/scielo.php?script=sci_arttext&pid=S0001-37652001000200004 |
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