Finite codimension stability of invariant surfaces

Abstract

Following recent work of T. Alazard and C. Shao 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 on the cohomological equation for translation flows.

Lemma 4.1 has been corrected after N. Tedesco pointed out a mistake in the calculations. The main results are unchanged