In this paper we are concerned with the existence of invariant curves for almost periodic reversible mappings with higher order degeneracy of the twist 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 $ q^n \varepsilon, $ rather than super exponential function.
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