The dynamics of the relativistic Kepler problem
Abouelmagd, Elbaz I. (National Research Institute of Astronomy and Geophysics. Astronomy Department (Egypt))
Guirao, Juan Luis Garcia (Universidad Politécnica de Cartagena. Departamento de Matemática Aplicada y Estadística)
Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)

Date:	2020
Abstract:	We deal with the Hamiltonian system (HS) provided by the correction given by the special relativity to the motion of the two-body problem, or by the first order correction to this problem coming from the general relativity. This Hamiltonian system is completely integrable with the angular momentum C and the Hamiltonian H. We have two objectives. First, we describe the global dynamics of the Hamiltonian system (HS) in the following sense. Let Ih and Ic are the subset of the phase space where H = h and C = c. Since C and H are first integrals, the sets Ic, Ih and Ihc = Ih∩Ic are invariant by the action of the flow of the Hamiltonian system (HS). We determine the global dynamics on those sets when h and c vary. Second, recently Tudoran in [21] provided a criterion which detects when a non-degenerate equilibrium point of a completely integrable system is Lyapunov stable. Every equilibrium point q of the completely integrable Hamiltonian system (HS) is degenerate and has zero angular momentum, so the mentioned criterion cannot be applied to it. But we will show that this criterion is also satisfied when it is applied to the Hamiltonian system (HS) restricted to zero angular momentum.
Grants:	Ministerio de Ciencia e Innovación PGC2018-097198-B-I00 Ministerio de Economía y Competitividad MTM2016-77278-P Ministerio de Economía y Competitividad MDM-2014-0445 Agència de Gestió d'Ajuts Universitaris i de Recerca 2017/SGR-1617 European Commission 777911
Note:	Altres ajuts: Fundación Séneca (Spain), grant 20783/PI/18
Rights:	Aquest document està subjecte a una llicència d'ús Creative Commons. Es permet la reproducció total o parcial, la distribució, la comunicació pública de l'obra i la creació d'obres derivades, fins i tot amb finalitats comercials, sempre i quan es reconegui l'autoria de l'obra original.
Language:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Subject:	Relativistic Kepler problem ; Global dynamics ; Lyapunov stability
Published in:	Results in Physics, Vol. 19 (December 2020) , art. 103406, ISSN 2211-3797

DOI: 10.1016/j.rinp.2020.103406

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Research literature > UAB research groups literature > Research Centres and Groups (research output) > Experimental sciences > GSD (Dynamical systems)
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