Following recent work of Alazard and Shao [AlSh] on applications of para-differential calculus to smooth conjugacy and stability problems for Hamiltonian systems, we prove finite codimension stability of invariant surfaces (in finite differentiability classes) of flat geodesic flows on translation surfaces. The result is also based on work of the author [F97, F21] on the cohomological equation for translation flows.
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Giovanni Forni (2026) studied this question.
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