  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 $f^*H\sim qH$ 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.
