An extension to the planar Markus-Yamabe Jacobian conjecture

TL;DR

This paper extends the planar Markus-Yamabe Jacobian Conjecture to include differential systems with Jacobian matrices whose eigenvalues have non-positive real parts, broadening the conjecture's scope.

Contribution

It introduces an extension to the classical conjecture, considering systems with Jacobian eigenvalues having zero or negative real parts, which was not previously addressed.

Findings

Extended the conjecture to include zero real parts

Provided theoretical framework for the extended conjecture

Potential implications for stability analysis in differential systems

Abstract

We extend the planar Markus-Yamabe Jacobian Conjecture to differential systems having jacobian matrix with eigenvalues with negative or zero real parts.