2022-06-282022-06-282022-05-23SÁNCHEZ, A. C. T. Equivalência entre o método de Melnikov e o método de Averaging para campos de vetores suaves por partes quase-integráveis. 2022. 117 f. Dissertação (Mestrado em Matemática) - Universidade Federal de Goiás, Goiânia, 2022.http://repositorio.bc.ufg.br/tede/handle/tede/12135In this work the equivalence between the Melnikov method and the Averaging method will be studied for a piecewise smooth near-integrable systems in n-dimensional spaces (n ≥ 2). We present an introduction of both methods, then we direct the study of these methods to piecewise smooth near-integrable systems and we show the equivalence between them, where a key step of solving this problem is to construct an appropriate change of coordinates, which transforms the perturbed piecewise smooth system into a periodic system. We also present the formula of the second order Melnikov function for planar piecewise near-Hamiltonian systems and we will finish the work with some applications of the results presented in a class of three-dimensional autonomous systems.Attribution-NonCommercial-NoDerivatives 4.0 InternationalPeriódicasCiclos limiteCampos de vetores suaves por partesAveraging methodMelnikov methodPeriodic solutionsLimit cyclesPiecewise smooth vector fieldsCIENCIAS EXATAS E DA TERRA::MATEMATICA::MATEMATICA APLICADADissertação