High Quality Content by WIKIPEDIA articles! The Andronov–Pontryagin criterion is a necessary and sufficient condition for the stability of dynamical systems in the plane. It was derived by Aleksandr Andronov and Lev Pontryagin in 1937. A dynamical system dot{x} = v(x), where v is a C1-vector field on the plane, x?R2 , is orbitally topologically stable if and only if the following two conditions hold: All equilibrium points and periodic orbits are hyperbolic. There are no saddle connections. The same statement holds if the vector field v is defined on the unit disk and is transversal to the boundary.

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