Persistence of Multiscale Degenerate Invariant Tori in Reversible Systems with Degenerate Frequency Mapping

This paper considers a class of nearly integrable reversible systems whose unperturbed part has a degenerate frequency mapping and a degenerate equilibrium point. Based on some KAM techniques and the topological degree theory, we prove the persistence of multiscale degenerate hyperbolic lower-dimensional invariant tori with prescribed frequencies.