Slow passage through a saddle-center bifurcation
The authors consider slowly varying conservative one-degree of freedom Hamiltonian systems in the case of a saddle-center bifurcation. By using energy-angle coordinates the equation is brought in standard form for the method of averaging. The averaged equation is used to obtain the boundary of the basin of repulsion. Further it is shown that the slow passage of the saddle-center homoclinic orbit consists of a large sequence of nearly saddle-center homoclinic orbits to the strongly nonlinear oscillations before and after the passage.
scientific article; zbMATH DE number 1439881