Eur. Phys. J. Plus (2011) 126: 104
https://doi.org/10.1140/epjp/i2011-11104-y

Regular Article

Relevance of the 1:1 resonance in galactic dynamics

¹ Dipartimento di Scienze di Base e Applicate per l’Ingegneria, Università di Roma “La Sapienza”, Via Antonio Scarpa, 16, 00161, Roma, Italy
² Dipartimento di Fisica, Università di Roma “Tor Vergata”, Via della Ricerca Scientifica, 1, 00133, Roma, Italy
³ Sezione di Roma Tor Vergata, INFN, Via della Ricerca Scientifica, 1, 00133, Roma, Italy

^* e-mail: pucacco@roma2.infn.it

Received: 6 September 2011
Accepted: 2 October 2011
Published online: 9 November 2011

Abstract

This paper aims to illustrate the applications of resonant Hamiltonian normal forms to some problems of galactic dynamics. We detail the construction of the 1:1 resonant normal form corresponding to a wide class of potentials with self-similar elliptical equipotentials and apply it to investigate relevant features of the orbit structure of the system. We show how to compute the bifurcation of the main periodic orbits in the symmetry planes of a triaxial ellipsoid and in the meridional plane of an axisymmetric spheroid and briefly discuss how to refine these results with higher-order approaches.