A topological characterization of omega-limit sets on dynamical systems

Hahng-Yun Chu, Ahyoung Kim, Jong-Suh Park

Published 2013-06-05Version 1

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 $\Omega$-limit set of a compact set is quasi-attracting.