On recurrent trajectories of autonomous differential inclusions (Q944408)

The authors consider the autonomous differential inclusion \(x' \in F(x)\) in some domain of a finite dimensional space, where the multi-function \(F\) has a continuity property and is bounded, closed and convex valued. They define the notion of generalized-periodic solution and prove the existence of such a solution on compact minimal sets. The results are then related to the notion of recurrent trajectory which goes back to Birkhoff, Carathéodory and Khinchin.