Campos descontínuos com chaveamento no Rn - Silva , Tharsis Souza (2016)
In this work we _rstly study a relay system X on the Rn that, under certain conditions, it has a one parameter family of 1-periodic orbits that arises in the origin and increase inde_nitely. We study yet another relay system class X_, that it is formed from the initial relay system by aditions of nilpotent parameters that, under certain conditions, it has the same result of the previous, and yet family of periodic orbits that arises in the origin and ends in a loop, or family that bifurcate of a loop and arise inde_nitelly. Furthermore the periodic solutions are explicitely given by Euler polynomials. Finally we study a third order di_erential equation with relay looking for periodic orbits of di_erent degrre of di_erentiability and this is done by the associated vector _eld with jump.