A Short Proof that Minimal Sets of Planar Ordinary Differential Equations are Trivial

TL;DR

This paper provides a concise proof, using the divergence theorem, demonstrating that minimal sets in planar ordinary differential equations are trivial, simplifying previous complex proofs in the field.

Contribution

It introduces a short, divergence theorem-based proof establishing the triviality of minimal sets in planar ODEs, offering a more straightforward approach.

Findings

Minimal sets in the plane are trivial.

The divergence theorem can be used to verify triviality.

Simplifies previous proofs in the field.

Abstract

We present a short proof, relaying on the divergence theorem, verifying that minimal sets in the plane are trivial.