Expansive flows of surfaces

TL;DR

This paper characterizes expansive flows on compact surfaces, showing they are composed of saddle singularities with dense separatrices and can be constructed via surgery on suspensions of minimal interval exchange maps.

Contribution

It provides a complete characterization of expansive flows on surfaces and links their structure to minimal interval exchange maps.

Findings

Expansive flows require saddle singularities with dense separatrices.

Such flows can be constructed through surgery on suspensions of minimal interval exchange maps.

The characterization is both necessary and sufficient.

Abstract

We prove that a flow on a compact surface is expansive if and only if the singularities are of saddle type and the union of their separatrices is dense. Moreover we show that such flows are obtained by surgery on the suspension of minimal interval exchange maps.