Franks' Lemma for C 2 Mane Perturbations of Riemannian Metrics and Applications to Persistence

A Lazrag (1) , Ludovic Rifford (2, 1) , Rafael Ruggiero (3)

1 LJAD - Laboratoire Jean Alexandre Dieudonné
2 McTAO - Mathematics for Control, Transport and Applications
3 departimento de matematica

Given a compact Riemannian manifold, we prove a uniform Franks' lemma at second order for geodesic flows and apply the result in persistence theory.

Domaines: Systèmes dynamiques [math.DS]

A Lazrag, Ludovic Rifford, Rafael Ruggiero. Franks' Lemma for C 2 Mane Perturbations of Riemannian Metrics and Applications to Persistence. Journal of modern dynamics, 2016, 10, pp.379-411. ⟨10.3934/jmd.2016.10.379⟩. ⟨hal-01111786⟩