Método de Melnikov generalizado e aplicações

• Autor(a) principal: Silva, Lucas Carvalho
• Data de Publicação: 2011
• Tipo de documento: Dissertação
• Idioma: por
• Título da fonte: LOCUS Repositório Institucional da UFV
• Texto Completo: http://locus.ufv.br/handle/123456789/4906
• topic: Sistemas dinâmicos; Método de Melnikov; Método de Melnikov generalizado; Melnikov-Gruendler; Dynamical systems; Melnikov method; Melnikov method generalized; Melnikov-Gruendler; CNPQ::CIENCIAS EXATAS E DA TERRA::MATEMATICA

We define a dynamic system as follows dx = f(x) + g(x, t, ε), x ∈ Rn (1) ____ dt where f : Rn → Rn e g : Rn x R x RN → Rn Rn are C2, g is periodic in t, such that the system x˙ = f(x) (2) has a hyperbolic saddle point and a homoclinic orbit associated to this point, (1) is called perturbed homoclinic system (PHS). What happens with the system (2) after a disturbance, ie, when we in (1) ε assume positive values? In this work we analyze some methods in order to answer this question. We study the classical method of Melnikov for systems when n = 2 and g is periodic in t, a method to eliminate the requirement that g is periodic in t and also a generalization of the classical method of Melnikov to higher dimensions, the method of Melnikov-Gruendler. For each case we present applications.