ENTROPY OF TWIST INTERVAL MAPS

We investigate the recently introduced notion of rotation numbers for periodic orbits of interval maps. We identify twist orbits, that is th ose orbits that are the simplest ones with given rotation number. We e stimate from below the topological entropy of a map having an orbit wi th given rotation number. Our estimates are sharp: there are unimodal maps where the equality holds. We also discuss what happens for maps w ith larger modality. In the Appendix we present a new approach to the problem of monotonicity of entropy in one-parameter families of unimod al maps.