Persistence of Degenerate Lower Dimensional Invariant Tori with Prescribed Frequencies in Reversible Systems

This paper considers small perturbations of an integrable reversible system which has a degenerated lower dimensional invariant torus in some sense. In the presence of some higher-order terms, by some KAM technique and the stability of critical points of real analytic functions developed for hamiltonian systems, we prove the persistence of the degenerate lower dimensional invariant torus with prescribed frequencies without extra conditions on the perturbations besides the smallness. This result is an extension of the partial result of hamiltonian systems in Xu and You (Regul Chaotic Dyn 25(6):616–650, 2020) to reversible systems.