Periodic orbits and equilibria for a seventh-order generalized Hénon-Heiles Hamiltonian system

In this paper we study analytically the existence of two families of periodic orbits using the averaging theory of second order, and the finite and infinite equilibria of a generalized Hénon-Heiles Hamiltonian system which includes the classical Hénon-Heiles Hamiltonian. Moreover we show that this g...

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Detalhes bibliográficos
Autores: Llibre, Jaume|||0000-0002-9511-5999, Saeed, Tareq, Zotos, Euaggelos E.|||0000-0002-1565-4467
Formato: artículo
Fecha de publicación:2021
País:España
Recursos:Universitat Autònoma de Barcelona
Repositorio:Dipòsit Digital de Documents de la UAB
Idioma:inglés
OAI Identifier:oai:ddd.uab.cat:257110
Acesso em linha:https://ddd.uab.cat/record/257110
https://dx.doi.org/urn:doi:10.1016/j.geomphys.2021.104290
Access Level:acceso abierto
Palavra-chave:Eneralized Hénon-Heiles potential
Finite equilibria
Infinite equilibria
Descrição
Resumo:In this paper we study analytically the existence of two families of periodic orbits using the averaging theory of second order, and the finite and infinite equilibria of a generalized Hénon-Heiles Hamiltonian system which includes the classical Hénon-Heiles Hamiltonian. Moreover we show that this generalized Hénon-Heiles Hamiltonian system is not C integrable in the sense of Liouville-Arnol'd, i.e. it has not a second C first integral independent with the Hamiltonian. The techniques that we use for obtaining analytically the periodic orbits and the non C Liouville-Arnol'd integrability, can be applied to Hamiltonian systems with an arbitrary number of degrees of freedom.