Wong-Zakai approximation for the dynamics of stochastic evolution equation driven by rough path with Hurst index $H\in(\frac{1}{3},\frac{1}{2}]$

In this paper, we obtain the existence of random attractors for a class of evolution equations driven by a geometric fractional Brownian rough path with Hurst index $H\in(\frac{1}{3},\frac{1}{2}]$ and establish the upper semi-continuity of random attractors $\mathcal{A}_η$ for the approximated systems of the evolution equations.