2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/98368It is well-known that on any Veech surface, the dynamics in any minimal direction is uniquely ergodic. In this paper it is shown that for any genus 2 translation surface which is not a Veech surface there are uncountably many minimal but not uniquely ergodic directions.15 pages, 2 figures, major simplifications in presentation as recommended by referee, to appear in Ergodic Theory Dynamical SystemsDynamical Systems37D40; 37E35text