Small perturbations of partially hyperbolic toral automorphisms with dense center foliation and a smooth center foliation are smoothly leaf-conjugate, and any bi-Hölder conjugacy is smooth.
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Center foliation rigidity for partially hyperbolic toral diffeomorphisms
Small perturbations of partially hyperbolic toral automorphisms with dense center foliation and a smooth center foliation are smoothly leaf-conjugate, and any bi-Hölder conjugacy is smooth.