C2 densely the 2-sphere has an elliptic closed geodesic

TL;DR

This paper proves that any C2 Riemannian metric on the 2-sphere or projective plane can be approximated by a smooth metric with an elliptic closed geodesic, contributing to the understanding of geodesic dynamics.

Contribution

It introduces a method to approximate C2 metrics on the 2-sphere or projective plane by smooth metrics with elliptic closed geodesics, advancing geometric analysis.

Findings

Any C2 metric can be approximated by smooth metrics with elliptic closed geodesics.

The result applies to both 2-sphere and projective plane.

Enhances understanding of geodesic flow stability.

Abstract

We prove that a riemannian metric on the 2-sphere or the projective plane can be C2-approximated by a smooth metric whose geodesic flow has an elliptic closed geodesic.