A Sharkovskii-type theorem for minimally forced interval maps

Abstract

We state and prove a version of Sharkovskiǐ's theorem for forced interval maps in which the forcing flow is minimal (Birkhoff recurrent). This setup includes quasiperiodically forced interval maps as a special case. We find that it is natural to substitute the concept of "fixed point" with that of "core strip." Core strips are frequently of almost automorphic type.