Thispaperconsidersthefollowingquestion:GivenanAnosovendomorphismfonT~m,whetherfistopologicallyconjugatetosomehyperbolictotalendomorphism?ItiswellknownthattheanswerforAnosovdiffeomorphismsandexpandingendomorphismsisaffirmative.HweverfortheremainderAnosovendomorphisms,aquitedifferentanswerisobtainedinthispaper,i.e.,forgenericAnosovendomorphisms,theyarenottopologicallyconjugatetoanyhyperbolictoralendomorphism.
