Hairiness of $\omega$-bounded surfaces with non-zero Euler characteristic

TL;DR

This paper proves that any flow on an omega-bounded surface with non-zero Euler characteristic must have a fixed point, contributing to the understanding of dynamical systems on non-metric manifolds.

Contribution

It establishes a fixed point theorem for flows on omega-bounded surfaces with non-zero Euler characteristic, extending classical results to a broader class of non-metric surfaces.

Findings

Any flow on such surfaces has a fixed point.

The result applies to omega-bounded surfaces with non-zero Euler characteristic.

Provides insights into the dynamics of non-metric manifolds.

Abstract

A little complement concerning the dynamics of non-metric manifolds is provided, by showing that any flow on an $\omega$-bounded surface with non-zero Euler character has a fixed point.