On the Hyperbolicity of Toral Endomorphisms

Nonsingular endomorphisms of the $m$-torus $\mathbb T^m$, $m\ge 2$, which are $C^1$ perturbations of linear hyperbolic endomorphisms are considered. Sufficient conditions for such maps to be hyperbolic (i.e., belong to the class of Anosov endomorphisms) are found.