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.