A Spectral Dichotomy Version of the Nonautonomous Markus--Yamabe Conjecture
\'Alvaro Casta\~neda, Gonzalo Robledo
TL;DR
This paper introduces a nonautonomous version of the Markus--Yamabe conjecture using spectral methods, proving it for specific cases and demonstrating global attractor properties in autonomous systems.
Contribution
It presents a novel nonautonomous formulation of the conjecture and proves its validity for scalar and triangular systems, expanding the theoretical understanding.
Findings
Conjecture verified for scalar systems
Conjecture verified for triangular systems
Origin is a global attractor in autonomous systems
Abstract
In this article we introduce a nonautonomous version of the Markus--Yamabe conjecture from an exponential dichotomy spectrum point of view. We prove the validity of this conjecture for the scalar and triangular case. Additionally we show that the origin is a global attractor for an autonomous system by using nonautonomous dynamical systems tools.
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