Bulletin of the
Korean Mathematical Society BKMS

In this paper, we introduce the concept of $\omega$-expansive of random map on compact metric spaces $\mathcal{P}$. Also we introduce the definitions of positively, negatively shadowing property and shadowing property for two-sided RDS. Then we show that if $\varphi$ is $\omega$-expansive and has the shadowing property for $\omega$, then $\varphi$ is topologically stable for $\omega$.

Keywords: $\omega$-expansive, shadowing property, topologically stable

MSC numbers: Primary 37H30, 37H12, 37B05

Supported by: This work was financially supported by MNUE. This work has been supported by Mongolian National University of Education.