Almost automorphic and almost periodic dynamics for
quasimonotone non-autonomous differential equations

with Sylvia Novo and Rafael Obaya,
J. Dynam. Differential Equations
17 (3) (2005), 589-619.

The occurrence of almost automorphic dynamics for monotone non-autonomous
recurrent finite-delay functional differential equations is analyzed. Topological methods
are used to ensure its presence in the case of existence of semicontinuous
semi-equilibria. When these semi-equilibria are continuous and strong, the presence
of almost automorphic extensions is persistent under small perturbations. The above
method provides a minimal set isomorphic to the base in the case of a convex
semiflow. Some examples show the applicability of these results.