Abstract
In this paper we generalize analytic studies the problems related tosuppression of chaos and non--feedback controlling chaotic motion.We develop an analytic method of the investigation of qualitativechanges in chaotic dynamical systems under certain external periodicperturbations. It is proven that for polymodal maps one canstabilize chosen in advance periodic orbits. As an example, thequadratic family of maps is considered. Also we demonstrate that for a piecewise linearfamily of maps and for a two-dimensional map having a hyperbolicattractor there are feedback-free perturbations which lead to thesuppression of chaos and stabilization of certain periodic orbits.
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