Non-existence of wandering intervals and structure of topological attractors of one dimensional dynamical systems: 1. The case of negative Schwarzian derivative

Abstract

AbstractIt 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.