On the existence of periodic orbits and KAM tori in the Sprott A system: a special case of the Nosé–Hoover oscillator
Carregando...
Arquivos
Data
Autores
Orientador
Coorientador
Pós-graduação
Curso de graduação
Título da Revista
ISSN da Revista
Título de Volume
Editor
Tipo
Artigo
Direito de acesso
Acesso aberto
Resumo
We consider the well-known Sprott A system, which is a special case of the widely studied Nosé–Hoover oscillator. The system depends on a single real parameter a, and for suitable choices of the parameter value, it is shown to present chaotic behavior, even in the absence of an equilibrium point. In this paper, we prove that, for a≠ 0 , the Sprott A system has neither invariant algebraic surfaces nor polynomial first integrals. For a> 0 small, by using the averaging method we prove the existence of a linearly stable periodic orbit, which bifurcates from a non-isolated zero-Hopf equilibrium point located at the origin. Moreover, we show numerically the existence of nested invariant tori surrounding this periodic orbit. Thus, we observe that these dynamical elements and their perturbation play an important role in the occurrence of chaotic behavior in the Sprott A system.
Descrição
Palavras-chave
Averaging method, Chaotic behavior, Invariant algebraic surfaces, Nested invariant tori, Nosé–Hoover oscillator, Periodic orbits, Sprott A system
Idioma
Inglês
Citação
Nonlinear Dynamics, v. 92, n. 3, p. 1287-1297, 2018.
