On the persistence of lower-dimensional tori in reversible systems with high dimensional degenerate equilibrium under small perturbations

Abstract

<p style='text-indent:20px;'>This paper focuses on the persistence of lower-dimensional tori in reversible systems with high dimensional degenerate equilibrium under small perturbations. By an improved KAM iteration and Topological degree theory, we prove that the invariant torus with given frequency persists under small perturbations. Our result is a generalization of X. Wang et al [On the persistence of degenerate lower-dimensional tori in reversible systems, Ergodic Theory Dynam. Systems, 35(2015), 2311-2333].</p>