For almost every direction on a translation surface, the invariant surface of the flat geodesic flow persists within a finite-codimension family of smooth Hamiltonian perturbations.
Bony, Calcul symbolique et propagation des singularit\'es pour les \'equations aux d\'eriv\'ees partielles non lin\'eaires Annales scientifiques de l’ \'E.N.S
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Finite codimension stability of invariant surfaces
For almost every direction on a translation surface, the invariant surface of the flat geodesic flow persists within a finite-codimension family of smooth Hamiltonian perturbations.