The Persistence of Degenerate Lower-Dimensional Tori in Reversible Systems with a Degenerate Normal Equilibrium Point

• DOI: 10.1007/s10884-021-10075-5
• Publication Date: 2021-09-21T09:02:59Z
• Authors: Ru Qu; DongFeng Zhang
• Keywords: Critical point (mathematics); Persistence (discontinuity); Kolmogorov–Arnold–Moser theorem; Equilibrium point

In this paper we consider the persistence of degenerate lower-dimensional tori in reversible systems with a degenerate normal equilibrium point, including hyperbolic and elliptic types. Based on the method of introducing external parameters, KAM iteration and implicit function theorem, we prove that if the perturbations are sufficiently small and frequency $$\omega _0$$ satisfies the Diophantine condition, the reversible system still has a lower-dimensional torus with frequency $$\omega _0$$ .