2014-07-292010-03-252010-03-05ROCHA, Valdomiro. On persistents centers. 2010. 69 f. Dissertação (Mestrado em Ciências Exatas e da Terra) - Universidade Federal de Goiás, Goiânia, 2010.http://repositorio.bc.ufg.br/tede/handle/tde/1966The problem of destingnishing whether a monodromic critical point with imaginary eigenvalues of a family of a planar analitical vector field is a center or a focus was already solved by Lyapunov. This is the famous center-focus problem which was solved by calculating the so-called Lyapunov constants and see whether or not they are zero. We present a few ways to calculate them acording the approaches that they use: camputation of a Lyapunov function; use of normal forms; computation of the power of expansion of a solution in polar coordinates; use of the algebraic structure of Lyapunov constants; method of Lyapunov-Schmit and Melnikov functions. Despite all of the above the centerfocus problem for a simple family as the cube is resisting all attempts at solution. For this reason the centers, we propose to grade the in three levels in order to make the problem more feasible.application/pdfAcesso AbertoEquações diferenciaisponto singularproblema centro-fococonstantes de Lyapunov.Differential Equationssingular pointcenter-focus problemLyapunov constants.CNPQ::CIENCIAS EXATAS E DA TERRA::MATEMATICA::GEOMETRIA E TOPOLOGIADissertação