  In the present work we obtain rigidity results analysing the set of regular
points, in the sense of Oseledec's Theorem. It is presented a study on the
possibility of an Anosov diffeomorphisms having all Lyapunov exponents defined
everywhere. We prove that this condition implies local rigidity of an Anosov
automorphism of the torus $\mathbb{T}^d, d \geq 3,$ $C^1-$close to a linear
automorphism diagonalizable over $\mathbb{R}$ and such that its characteristic
polynomial is irreducible over $\mathbb{Q}.$
