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

Autor:	Orestes Bueno, Liliana Puchuri
Rok vydání:	2016
Předmět:	Applied Mathematics Infinitesimal 010102 general mathematics Mathematical analysis First integrals 01 natural sciences 010101 applied mathematics symbols.namesake Quadratic equation symbols Projective plane 0101 mathematics Hamiltonian (quantum mechanics) Analysis Linear perturbation Mathematics
Zdroj:	Journal of Differential Equations. 261:7157-7193
ISSN:	0022-0396
DOI:	10.1016/j.jde.2016.09.019
Popis:	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.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::4367fe5ddaf13b05aae8bcc6cf3b5808 https://doi.org/10.1016/j.jde.2016.09.019 Zobrazit plný text záznamu Full Text from ScienceDirect