Periodic orbits near equilibria via averaging theory of second order

Lyapunov, Weinstein and Moser obtained remarkable theorems giving sufficient conditions for the existence of periodic orbits emanating from an equilibrium point of a differential system with a first integral. Using averaging theory of first order we established in [1] a similar result for a differen...

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Detalhes bibliográficos
Autores: Barreira, Luis|||0000-0003-4655-5792, Llibre, Jaume|||0000-0002-9511-5999, Valls, Clàudia|||0000-0001-8279-1229
Formato: artículo
Fecha de publicación:2012
País:España
Recursos:Universitat Autònoma de Barcelona
Repositorio:Dipòsit Digital de Documents de la UAB
Idioma:inglés
OAI Identifier:oai:ddd.uab.cat:150561
Acesso em linha:https://ddd.uab.cat/record/150561
https://dx.doi.org/urn:doi:10.3846/13926292.2012.736090
Access Level:acceso abierto
Palavra-chave:Periodic orbit
Averaging theory of second order
Hopf bifurcation
Descrição
Resumo:Lyapunov, Weinstein and Moser obtained remarkable theorems giving sufficient conditions for the existence of periodic orbits emanating from an equilibrium point of a differential system with a first integral. Using averaging theory of first order we established in [1] a similar result for a differential system without assuming the existence of a first integral. Now, using averaging theory of second order, we extend our result to the case when the first order average is identically zero. Our result can be interpreted as a kind of special Hopf bifurcation.