On the approach of Holmes and Sanders to the Melnikov procedure in the method of averaging (Q801454)

A two-dimensional system (1) \(\dot x=\mu f(t,x,\mu)=\mu f_ 1(x)+\mu^ 2f_ 2(t,x)+..\). is considered where f is periodic in t and \(\mu >0\) is a small parameter. Under the assumption that the equation \(\dot x=\mu f_ 1(x)\) admits two hyperbolic equilibria the author derives a Melnikov type formula for the description of the invariant manifolds of (1).