Minimal geodesics and topological entropy on T^2

TL;DR

This paper proves that on any Riemannian torus, the topological entropy of the geodesic flow restricted to minimal geodesics is zero, regardless of the metric chosen, highlighting a fundamental property of such flows.

Contribution

It establishes a metric-independent result showing the vanishing of topological entropy for minimal geodesics on Riemannian tori.

Findings

Topological entropy of minimal geodesics is zero

Result holds for any Riemannian metric on T^2

Highlights a fundamental property of geodesic flows on tori

Abstract

Let (T^2, g) be a two-dimensional Riemannian torus. In this paper we prove that the topological entropy of the geodesic flow restricted to the set of initial conditions of minimal geodesics vanishes, independent of the choice of the Riemannian metric.