Robustly transitive maps with critical points and large dimensional central spaces

Abstract

Given any triplet of positive integers n ≥ 2, m and k such that n = m + k, we exhibit a C1 robustly transitive endomorphism of Tn with persistent critical points in the isotopy class of F ×Id, where F is an expanding map of Tm and Id is the identity of Tk. Furthermore, if k is small, the map is not only in the isotopy class but in fact a perturbation of F × Id.