Unstable States for Closed String with Massive Point

The stability problem for the hypocycloidal rotational states of the closed relativistic string with a point-like mass is solved with the help of analysis of small disturbances of these states. Both analytical and numerical investigations showed an unexpected result: the mentioned states turned out to be unstable. This conclusion is based upon the presence of roots with positive imaginary parts (increments) in the spectrum of frequencies of small disturbances. But these increments were small enough, so this instability had not been detected in previous numerical experiments. For the linear rotational states (the particular case of hypocycloidal states) the stability was confirmed. These results are important for applications of this model in hadron spectroscopy.