Periodic orbits for a generalized Hénon-Heiles Hamiltonian system with an additional singular gravitational term
Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Valls, Clàudia 1973- (Universidade de Lisboa. Instituto Superior Técnico. Departamento de Matemàtica)

Date:	2021
Abstract:	We study the periodic dynamics of the Hénon-Heiles Hamiltonian system with the additional singular gravitational term 1/(x2+y2). The Hénon-Heiles modelizes how stars move around a galactic center. The addition of this singular gravitational term allows to modelize the motion of the stars in a pseudo or post-Newtonian dynamics. Thus this model allows to predict phenomena which cannot be detected by the classical Newtonian mechanics. Using the averaging theory of first order we study analytically the existence of two families of periodic orbits of this generalized Hénon-Heiles Hamiltonian system. Moreover we characterize when this generalized Hénon-Heiles Hamiltonian system has or has not a second C 1 first integral independent of the Hamiltonian.
Grants:	Agencia Estatal de Investigación PID2019-104658GB-I00 Agència de Gestió d'Ajuts Universitaris i de Recerca 2017/SGR-1617 European Commission 777911
Rights:	Tots els drets reservats.
Language:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Subject:	Generalized Henon-Heiles potential ; Periodic orbits ; Averaging theory
Published in:	Europhysics Letters (EPL), Vol. 134, Issue 6 (June 2021) , art. 60005, ISSN 1286-4854

DOI: 10.1209/0295-5075/134/60005

Postprint 9 p, 545.5 KB

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