A topological characterization of omega-limit sets on dynamical systems
In this article, we deal with several notions in dynamical systems. Firstly, we prove that both closure function and orbital function are idempotent on set-valued dynamical systems. And we show that the compact limit set of a connected set is also connected. Furthermore, we prove that the $Ω$-limit set of a compact set is quasi-attracting.
math.DS↗