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On the classification of elliptic foliations induced by real quadratic fields with center

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dc.contributor.author Puchuri, Liliana es_PE
dc.contributor.author Bueno, Orestes es_PE
dc.date.accessioned 2024-05-30T23:13:38Z
dc.date.available 2024-05-30T23:13:38Z
dc.date.issued 2016
dc.description.abstract Related to the study of Hilbert's infinitesimal problem, is the problem of determining the existence and estimating the number of limit cycles of the linear perturbation of Hamiltonian fields. A classification of the elliptic foliations in the projective plane induced by the fields obtained by quadratic fields with center was already studied by several authors. In this work, we devise a unified proof of the classification of elliptic foliations induced by quadratic fields with center. This technique involves using a formula due to Cerveau & Lins Neto to calculate the genus of the generic fiber of a first integral of foliations of these kinds. Furthermore, we show that these foliations induce several examples of linear families of foliations which are not bimeromorphically equivalent to certain remarkable examples given by Lins Neto. (C) 2016 Elsevier Inc. All rights reserved.
dc.description.sponsorship Consejo Nacional de Ciencia, Tecnología e Innovación Tecnológica - Concytec
dc.identifier.doi https://doi.org/10.1016/j.jde.2016.09.019
dc.identifier.uri https://hdl.handle.net/20.500.12390/2885
dc.language.iso eng
dc.publisher Elsevier BV
dc.relation.ispartof JOURNAL OF DIFFERENTIAL EQUATIONS
dc.rights info:eu-repo/semantics/openAccess
dc.subject Applied Mathematics
dc.subject Analysis es_PE
dc.subject.ocde http://purl.org/pe-repo/ocde/ford#1.01.01
dc.title On the classification of elliptic foliations induced by real quadratic fields with center
dc.type info:eu-repo/semantics/article
dspace.entity.type Publication
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