Bifurcation of the quasinormal spectrum and zero damped modes for rotating dilatonic black holes

It has been recently found that for the near extremal Kerr black holes appearing of zero damped modes (accompanied by quasinormal mode branching) signifies about inapplicability of the regime of small perturbations and the onset of turbulence. Here we show that this phenomenon is not limited by Kerr or Kerr-Newman solutions only, but also takes place for rotating dilatonic black holes for which we have found zero damped modes both numerically and analytically. We have also shown that, contrary to recent claims, there is no instability of a charged massive scalar field in the background of the rotating dilatonic black hole under physically adequate boundary conditions. Analytic expression for dominant quasinormal frequencies is deduced in the regime of large coupling $qQ$, where q and Q are the field and black hole charges, respectively.