Dynamical chaos in the problem of magnetic jet collimation

We investigate dynamics of a jet collimated by magneto-torsional oscillations. The problem is reduced to an ordinary differential equation containing a singularity and depending on a parameter. We find a parameter range for which this system has stable periodic solutions and study bifurcations of these solutions. We use Poincar\'e sections to demonstrate existence of domains of regular and chaotic motions. We investigate transition from periodic to chaotic solutions through a sequence of period doublings.