2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/139110In this paper the authors find examples of translation surfaces that have infinitely generated Veech groups, satisfy the topological dichotomy property that for every direction either the flow in that direction is completely periodic or minimal, and yet have minimal but non uniquely ergodic directions.25 pages, 6 figures. This revision contains an improved main theorem, simplified proofs, and an application to rational billiardsDynamical SystemsMathematical Physics32G15; 30F30; 30F60; 58F18text