If the Jacobian matrix of a dynamical system at a fixed point is Hurwitz, then the fixed point is asymptotically stable.
Markus-Yamabe conjecture asks if a similar result holds globally.
Precisely, the conjecture states that if a continuously differentiable map on an
-dimensional real vector space has a fixed point, and its Jacobian matrix is everywhere Hurwitz, then the fixed point is globally stable.
Related mathematical results concerning global asymptotic stability, which are applicable in dimensions higher than two, include various autonomous convergence theorems.