2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/168060We consider two C^2 Anosov diffeomorphisms in a C^1 neighborhood of a linear hyperbolic automorphism of three dimensional torus with real spectrum. We prove that they are C^1+ conjugate if and only if the differentials of the return maps at corresponding periodic points have the same eigenvalues.Several minor errors are fixed. 18 pages, 6 figures. Comments are welcomeDynamical Systems37C15, 37D20text