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.
Orbital topological stability of a dynamical system means that for any sufficiently small perturbation (in the C1-metric), there exists a homeomorphism close to the identity map which transforms the orbits of the original dynamical system to the orbits of the perturbed system (cf structural stability).
A zero of a vector field v, i.e. a point x0 where v(x0)=0, is said to be hyperbolic if none of the eigenvalues of the linearization of v at x0 is purely imaginary.
Finally, saddle connection refers to a situation where an orbit from one saddle point enters the same or another saddle point, i.e. the unstable and stable separatrices are connected (cf homoclinic orbit and heteroclinic orbit).