### Contracting endomorphisms and dualizing complexes

We investigate how one can detect the dualizing property for a chain complex over a commutative local Noetherian ring $R$. Our focus is on homological properties of contracting endomorphisms of $R$, e.g., the Frobenius endomorphism when $R$ contains a field of positive characteristic. For instance, in this case, when $R$ is $F$-finite and $C$ is a semidualizing $R$-complex, we prove that the following conditions are equivalent: (i) $C$ is a dualizing $R$-complex; (ii) $C\sim \mathbf{R}{\mathrm{Hom}}_{R}{(}^{n}R,C)$ for some $n>0$; (iii) ${\mathrm{G}}_{C}{\text{-dim}}^{n}R<\infty $ and $C$ is derived $\mathbf{R}{\mathrm{Hom}}_{R}{(}^{n}R,C)$-reflexive...