Abstract
In this paper we prove the existence of invariant curves for analytic reversible mappings under Brjuno–Russmann’s non-resonant condition. In the proof we use the polynomial structure of function to truncate, introduce a parameter $$q$$ and make the steps of KAM iteration infinitely small in the speed of function $$q^{n}\epsilon ,0 <q<1, $$ rather than super exponential function.
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