Regularity of time-preserving conjugacies for contact Anosov flows withC¹-Anosov splitting

Let (resp. ) be a smooth contact flow on a compact manifold V 1 (resp.) V 2 with Anosov splitting of class C 1 . We show that every time-preserving conjugacy Λ:( V 1 , )→( V 2 , ) is necessarily of class C 2 .