Abstract:
We address the problem of the conditions under which an  endomorphism(non-invertible map) having a dense orbit ensures that a sufficiently close perturbed map also exhibits a dense orbit.
In this context, we give sufficient conditions, which cover a large class of examples, for endomorphisms on the n-dimensional torus to be robustly transitive: the endomorphism must be volume expanding and any large connected arc must contain a point such that its future orbit belongs to an expanding region.
(Joint work with E. Pujals)

If we have enough time, I will show some ergodic properties for a generic subset of  this class of maps. More concretely, the existence of interesting measures such as ergodic expanding invariant measures with full support and exhibiting exponential decay of correlations.
(Joint work with V. Pinheiro and P.Varandas) 

Some examples will be shown.