an endomorphism on a normal projective variety x is said to be polarized if the pullback of an ample divisor a is linearly equivalent to qa, for some integer q>1. examples of these endomorphisms are naturally found in toric varieties and abelian varieties. indeed, it is conjectured that if x admits a polarized endomorphism, then x is a finite quotient of a toric fibration over an abelian variety. in this talk, we will restrict to the case of log calabi-yau pairs (x,b). we prove that if (x,b) admits a polarized endomorphism that preserves the boundary structure, then (x,b) is a finite quotient of a toric log calabi-yau fibration over an abelian variety. this is joint work with joaquin moraga and wern yeong.