Oscillations non linéaires des polytropes magnétiques

The paper includes a qualitative study of the equation of radial, nonlinear, nonadiabatic pulsations of the magnetic polytropes. The magnetic field is considered to be purely toroidal and weak. The nonadiabatic effects are described by two parameters μ related to the sources of energy and λ proportional with the damping of the energy. We find that there is only one equilibrium point for this equation. Its character is determined by μ. Whatever the values of the parameters involved, periodic orbits exist if μ > 0. These are unique and stable only if μ and λ are small. We note that in our qualitative analysis a major role is played by μ, λ is assumed to be small based on observational grounds. Numerical examples confirm and complete the qualitative analysis.