2022-11-072022-11-072022-09-30ALVES, A. M. Limit cycles in planar piecewise smooth systems having non-regular switches, time scales or rotated properties. 2022. 112 f. Tese (Doutorado em Matemática) - Universidade Federal de Goiás, Goiânia, 2022.http://repositorio.bc.ufg.br/tede/handle/tede/12415In this thesis, periodic trajectories in planar discontinuous piecewise linear systems with a nonregular switching line are studied. We provide sharp upper bounds of one or two limit cycles for certain classes of the model considered. We also establish the stability and hyperbolicity of these limit cycles. In addition, we provide examples reaching one and two limit cycles for these classes. We perform the global analysis of a representative model through bifurcation theory to analyze the birth of limit cycles, sliding periodic trajectories, and tangential ones. We also provide some results addressing the coexistence of periodic trajectories. We studied Fast-Slow systems with nonregular switching line with a new approach. This study allows proving that a specific sliding periodic trajectory is in fact a homoclinic trajectory. This homoclinic trajectory arises from a bifurcation of sliding limit cycles that are not topologically equivalents. We propose the theory of piecewise rotated vector fields with the goal of understanding how the trajectories of two families of rotated vector fields behave as the same parameter is varied. In this context, we prove the non-intersection theorem for closed periodic trajectories for piecewise rotated vector fields.Attribution-NonCommercial-NoDerivatives 4.0 InternationalCampos de vetores suaves por partesTrajetórias periódicasSistemas rápido-lentoCampos de vetores rodados por partesTeoria de bifurcaçãoPiecewise smooth vector fieldsPeriodic trajectoriesFast-slow systemsPiecewise rotated vector fieldsBifurcation theoryCIENCIAS EXATAS E DA TERRA::MATEMATICATese