2014-07-292011-10-272011-03-25SILVA, Thársis Souza. Piecewise differential equation: limit cycles and invariant cones. 2011. 152 f. Dissertação (Mestrado em Ciências Exatas e da Terra) - Universidade Federal de Goiás, Goiânia, 2011.http://repositorio.bc.ufg.br/tede/handle/tde/1945In this work, we consider classes of discontinuous piecewise linear systems in the plane and continuous in the space. In the plane, we analyze systems of focus-focus (FF), focusparabolic (FP) and parabolic-parabolic (PP) type, separated by the straight line x = 0, and we prove that can appear until two limit cycles depending of parameters variations. Also we study a specific system, piecewise, with two saddles (one fixed in the origin and the other in the neighborhood of point (1;1)) separated by the straight line y= -x+1, and we show that can appear until two limit cycles depending of parameters variations. Finally, we examine a continuous piecewise linear system in R³ and we prove the existence of invariant cones and, through this structures, we determine some stable and unstable behavior.application/pdfAcesso AbertoSistemas lineares por partesCiclo limiteAplicações de PoincaréSelas hiperbólicasCones invariantesPiecewise linear systemsLimit cyclePoincaré mapsHyperbolic saddlesInvariant cones1. Sistema linear por partes; 2. Combinação de duas selas; 3.Cones InvariantesCNPQ::CIENCIAS EXATAS E DA TERRA::MATEMATICA::GEOMETRIA E TOPOLOGIADissertação