Periodic Orbits in Analytical Planar Galactic Potentials

We study the regular families of periodic orbits in an analytical planar galactic potential, using the method of Lindstedt. We obtain analytical expressions describing these orbits, validity of which is not limited to small amplitudes. We can delimit, in the space of the parameters, the domain of existence of each family of orbits. This revised version was published online in July 2006 with corrections to the Cover Date.