High Quality Content by WIKIPEDIA articles! In mathematics, the Markus-Yamabe conjecture is a conjecture on global asymptotic stability. The conjecture states that if a continuously differentiable map on an n-dimensional real vector space has a single fixed point, and its Jacobian matrix is everywhere Hurwitz, then the fixed point is globally stable. The conjecture is true for the two-dimensional case. However, counterexamples have been constructed in higher dimensions. Hence, in the two-dimensional case only, it can also be referred to as the Markus-Yamabe theorem.

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