In this paper we generalize analytic studies the problems related to
suppression of chaos and non--feedback controlling chaotic motion.
We develop an analytic method of the investigation of qualitative
changes in chaotic dynamical systems under certain external periodic
perturbations. It is proven that for polymodal maps one can
stabilize chosen in advance periodic orbits. As an example, the
quadratic family of maps is considered.
Also we demonstrate that for a piecewise linear
family of maps and for a two-dimensional map having a hyperbolic
attractor there are feedback-free perturbations which lead to the
suppression of chaos and stabilization of certain periodic orbits.