One-Dimensional Monotone Nonautonomous Dynamical Systems

In the paper of W. Shen and Y. Yi (J Differ Equ 122:114–136, 1995) a description of the structure of the omega limit set of a one-dimensional monotone nonautonomous dynamical system with a minimal almost periodic base is given. In particular, it has been proved that the omega limit set of such systems contains at most two minimal sets. In the article (Stark (Dyn Syst 18(4):351–364, 2003)) (see also the bibliography therein), J. Stark studies the dynamics of quasiperiodically forced monotone maps (namely, invariant sets, pinched and minimal sets, global attractors, and other questions).