Stability and Symmetry Breaking for Closed String with Massive Point

The closed relativistic string carrying a point-like mass in the space with nontrivial geometry is considered. For rotational states of this system (resulting in non-trivial Regge trajectories) the stability problem is solved. It was shown that rotations of the folded string with the massive point placed at the rotational center are stable (with respect to small disturbances) if the mass exceeds some critical value: $m>m_{cr}$. But these rotational states are unstable in the opposite case $m<m_{cr}$. We can treat this effect as the spontaneous symmetry breaking for the string state. Other classes of rotational motions of this system have appeared to be stable. These results were obtained both in numerical experiments and the analytical investigation of small disturbances for the rotational states.