A persistently singular map of T n that is C 2 robustly transitive but is not C 1 robustly transitive. (English)

Consider the high dimensional torus T n and the set E of its endomorphisms. We construct a map in E that is robustly transitive if E is endowed with the C 2 topology but is not robustly transitive if E is endowed with the C 1 topology.