New classes of C 1-robustly transitive maps with persistent critical points

Abstract

Recently, the authors proved in [C. Lizana and W. Ranter, Topological obstructions for robustly transitive endomorphisms on surfaces, Adv. Math. 390 (2021), pp. 107901] that every C 1 -robustly transitive toral endomorphism displaying critical points must be homotopic to a linear endomorphism having at least one eigenvalue with modulus greater than one. Here, we exhibit some examples of C 1 -robustly transitive surface endomorphisms displaying critical points in certain homotopy classes.