A solution to Flinn's conjecture on weakly expansive flows

TL;DR

This paper disproves Flinn's conjecture by demonstrating that weakly expansive flows are not necessarily expansive, using the horocycle flow on compact Riemann surfaces of negative curvature.

Contribution

The paper provides a counterexample to Flinn's conjecture, showing that weakly expansive flows do not always imply expansiveness.

Findings

Counterexample to Flinn's conjecture using horocycle flow

Weakly expansive flows are not necessarily expansive

Disproves a long-standing conjecture from 1972

Abstract

In L.W. Flinn's PhD thesis published in 1972, the author conjectured that weakly expansive flows are also expansive flows. In this paper we use the horocycle flow on compact Riemann surfaces of constant negative curvature to show that Flinn's conjecture is not true.