Franks' lemma for $\mathbf{C}^2$-Mañé perturbations of Riemannian metrics and applications to persistence
Rafael O. Ruggiero, Ludovic Rifford, Ayadi Lazrag · Journal of Modern Dynamics · 2016
We prove a uniform Franks' lemma at second order for geodesic flows on a compact Riemannian manifold and apply the result in persistence theory. Our approach, which relies on techniques from geometric control theory, allows us to show that Mañé (i.e., conformal) perturbations of the metric are sufficient to achieve the result.