Ergodic Theory and Dynamical Systems

Research Article

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

M. Yu. Lyubicha1

a1 Steklov Mathematical Institute (Leningrad Department), Fontanka 27, Leningrad 191011, USSR

Abstract

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)