Limit cycles of discontinuous piecewise polynomial vector fields

de Carvalho, Tiago [UNESP]Llibre, JaumeTonon, Durval José2018-12-112018-12-112017-05-01Journal of Mathematical Analysis and Applications, v. 449, n. 1, p. 572-579, 2017.1096-08130022-247Xhttp://hdl.handle.net/11449/169315When the first average function is non-zero we provide an upper bound for the maximum number of limit cycles bifurcating from the periodic solutions of the center x˙=−y((x2+y2)/2)m and y˙=x((x2+y2)/2)m with m≥1, when we perturb it inside a class of discontinuous piecewise polynomial vector fields of degree n with k pieces. The positive integers m, n and k are arbitrary. The main tool used for proving our results is the averaging theory for discontinuous piecewise vector fields.572-579engAveraging theoryCyclicityLimit cyclePiecewise smooth vector fieldsLimit cycles of discontinuous piecewise polynomial vector fieldsArtigo10.1016/j.jmaa.2016.11.048Acesso restrito2-s2.0-85008221893