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 $q$, $0 \lt q \lt 1$, which makes the steps of the KAM iteration infinitely small in the speed of function $q^n \varepsilon$, rather than super exponential function.
This pape was partially supported by the National Natural Science Foundation of China (11901131), Guizhou Provincial Science and Technology Foundation (1Y006).
"Existence of Invariant Curves for Degenerate Quasi-periodic Reversible Mappings." Taiwanese J. Math. 26 (4) 765 - 798, August, 2022. https://doi.org/10.11650/tjm/220201