2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/219998It is known that piecewise affine surface homeomorphisms always have measures of maximal entropy. This is easily seen to fail in the discontinuous case. Here we describe a piecewise affine, globally continuous surface map with no measure of maximal entropy.11 pages; 13 color figuresDynamical Systems37A35; 37A40; 37E99text