Equivalência entre o método de Melnikov e o método de Averaging para campos de vetores suaves por partes quase-integráveis

• Autor(a) principal: Tunubalá Sánchez, Angela Carolina
• Data de Publicação: 2022
• Tipo de documento: Dissertação
• Idioma: por
• Título da fonte: Repositório Institucional da UFG
• Texto Completo: http://repositorio.bc.ufg.br/tede/handle/tede/12135
• topic: Periódicas; Ciclos limite; Campos de vetores suaves por partes; Averaging method; Melnikov method; Periodic solutions; Limit cycles; Piecewise smooth vector fields; CIENCIAS EXATAS E DA TERRA::MATEMATICA::MATEMATICA APLICADA

In 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.