Franks' Lemma for C^2-Man\'e Perturbations of Riemannian Metrics and Applications to Persistence

TL;DR

This paper establishes a second-order version of Franks' lemma for geodesic flows on compact Riemannian manifolds and demonstrates its applications in persistence theory, advancing the understanding of metric perturbations.

Contribution

It introduces a uniform second-order Franks' lemma for geodesic flows and applies it to persistence theory, bridging geometric perturbations with topological stability.

Findings

Proved a second-order Franks' lemma for geodesic flows.

Applied the lemma to persistence theory.

Enhanced understanding of metric perturbations in Riemannian geometry.

Abstract

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