Existence of Invariant Curves for Degenerate Quasi-periodic Reversible Mappings

Abstract

In this paper we are concerned with the existence of invariant curves of quasi-periodic reversible mappings with higher order degeneracy of the twist condition under the Brjuno–Rüssmann’s non-resonant condition. In the proof we use a new variant of the KAM theory, containing an artificial parameter q, 0 < q < 1, which makes the steps of the KAM iteration infinitely small in the speed of function qε, rather than super exponential function.