A note on the divergence-free Jacobian Conjecture in R^2

TL;DR

This paper provides a shorter proof of a recent result related to the divergence-free Jacobian Conjecture in two-dimensional real space, connecting it to the global asymptotic stability Jacobian Conjecture and extending previous findings.

Contribution

It offers a more concise proof of a key result in the divergence-free Jacobian Conjecture and extends related results from prior work by Neuberger.

Findings

Shorter proof of Neuberger's result in R^2

Extension of previous results on divergence-free Jacobian Conjecture

Connection to global asymptotic stability Jacobian Conjecture

Abstract

We give a shorter proof to a recent result by Neuberger, in the real case. Our result is essentially an application of the global asymptotic stability Jacobian Conjecture. We also extend some of the results presented in Neuberger.