Poincareʹs recurrence theorems for set-valued dynamical systems Original Research Article

In this paper, we introduce a new concept called ‘a pair of coincident invariant measures’ and establish the existence of coincident invariant measures for set-valued dynamical systems. As applications, we first give the existence of minimal invariant measures (see definition below) for a set-valued mapping, and then set-valued versions of Poincareʹs recurrence theorems are also derived.