a1 Steklov Mathematical Institute (Leningrad Department), Fontanka 27, Leningrad 191011, USSR
It is proved that an arbitrary one dimensional dynamical system with negative Schwarzian derivative and non-degenerate critical points has no wandering intervals. This result implies a rather complete view of the dynamics of such a system. In particular, every minimal topological attractor is either a limit cycle, or a one dimensional manifold with boundary, or a solenoid. The orbit of a generic point tends to some minimal attractor.
(Received November 10 1987)
(Revised September 29 1988)