https://doi.org/10.1140/epjp/i2013-13021-5
Regular Article
The symmetric 1:2 resonance
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” and INFN, Sezione di Roma Tor Vergata, Via della Ricerca Scientifica, 1, 00133, Rome, Italy
* e-mail: pucacco@roma2.infn.it
Received:
1
August
2012
Accepted:
22
January
2013
Published online:
21
February
2013
This paper illustrates the application of the Lie transform normal-form theory to the construction of the 1:2 resonant normal form corresponding to a wide class of natural Hamiltonian systems. We show how to compute the bifurcations of the main periodic orbits in a potential with double-reflection symmetries. The stability analysis of the normal modes and of the periodic orbits in general position allows us to get overall information on the phase-space structure of systems in which this resonance is dominating. As an example we apply these results to a class of models useful as galactic potentials.
© Società Italiana di Fisica and Springer-Verlag Berlin Heidelberg, 2013