  Let $X$ be a klt projective variety with numerically trivial canonical
divisor. A surjective endomorphism $f:X\to X$ is amplified
(resp.~quasi-amplified) if $f^*D-D$ is ample (resp.~big) for some Cartier
divisor $D$. We show that after iteration and equivariant birational
contractions, an quasi-amplified endomorphism will descend to an amplified
endomorphism.
  As an application, when $X$ is Hyperk\"ahler, $f$ is quasi-amplified if and
only if it is of positive entropy. In both cases, $f$ has Zariski dense
periodic points. When $X$ is an abelian variety, we give and compare several
cohomological and geometric criteria of amplified endomorphisms and
endomorphisms with countable and Zariski dense periodic points (after an
uncountable field extension).
