Periodic orbits and equilibria for a seventh-order generalized Hénon-Heiles Hamiltonian system
Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Saeed, Tareq (King Abdulaziz University. Department of Mathematics (Saudi Arabia))
Zotos, Euaggelos E. (Aristotle University of Thessaloniki. Department of Physics)

Date:	2021
Abstract:	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.
Grants:	Agencia Estatal de Investigación MTM2016-77278-P Agència de Gestió d'Ajuts Universitaris i de Recerca 2017/SGR-1617 European Commission 777911
Rights:	Aquest document està subjecte a una llicència d'ús Creative Commons. Es permet la reproducció total o parcial, la distribució, i la comunicació pública de l'obra, sempre que no sigui amb finalitats comercials, i sempre que es reconegui l'autoria de l'obra original. No es permet la creació d'obres derivades.
Language:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Subject:	Eneralized Hénon-Heiles potential ; Finite equilibria ; Infinite equilibria
Published in:	Journal of geometry and physics, Vol. 167 (September 2021) , art. 104290, ISSN 0393-0440

DOI: 10.1016/j.geomphys.2021.104290

Postprint 13 p, 650.6 KB

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