  Let $X$ be a normal projective variety admitting a polarized endomorphism
$f$, i.e., $f^*H\sim qH$ for some ample divisor $H$ and integer $q>1$. It was
conjectured by Broustet and Gongyo that $X$ is of Calabi-Yau type, i.e.,
$(X,\Delta)$ is lc for some effective $\mathbb{Q}$-divisor such that
$K_X+\Delta\sim_{\mathbb{Q}} 0$. In this paper, we establish a general
guideline based on the equivariant minimal model program and the canonical
bundle formula. In this way, we prove the conjecture when $X$ is a smooth
projective threefold.
