Melnikov distance
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Consider a smooth dynamical system , with and g(t) periodic with period T. Suppose for ε = 0 the system has a hyperbolic fixed point x0 and a homoclinic orbit φ(t) corresponding to this fixed point. Then for sufficiently small there exists a T-periodic hyperbolic solution. The stable and unstable manifolds of this periodic solution intersect transversally. The distance between these manifolds measured along a direction that is perpendicular to the unperturbed homoclinc orbit φ(t) is called the Melnikov distance. If d(t) denotes this distance, then d(t) = ε(M(t) + O(ε)). The function M(t) is called the Melnikov function.