Existence of Invariant Curves for Degenerate Quasi-periodic Reversible Mappings

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