Lyapunov–Schmidt Approach to Studying Homoclinic Splitting in Weakly Perturbed Lagrangian and Hamiltonian Systems - Prykarpatsky, A. K.; Samoilenko, A. M.; Samoilenko, V. G. (Ukrains’kyi Matematychnyi Zhurnal, 2003)
We analyze the geometric structure of the Lyapunov–Schmidt approach to studying critical manifolds of weakly perturbed Lagrangian and Hamiltonian systems.