Building blocks of amplified endomorphisms of normal projective varieties

Let $X$ be a normal projective variety. A surjective endomorphism $f:X\to X$ is int-amplified if $f^{\ast }L-L=H$ for some ample Cartier divisors $L$ and $H$. This is a generalization of the so-called polarized endomorphism which requires that $f^{\ast }H\sim qH$ for some ample Cartier divisor $H$ and $q>1$. We show that this generalization keeps all nice properties of the polarized case in terms of the singularity, canonical divisor, and equivariant minimal model program.