Invariant curves for non-twist quasi-periodic reversible mappings with its application

In this paper, we consider the existence of invariant curves of non-twist reversible mappings which are quasi-periodic in the angle variables with the frequency ω = (ω1, ω2, …, ωm). We prove that the mapping possesses an invariant curve with rotation number γ belonging to the image set of frequency function, when ω and 2πγ−1 satisfy Diophantine condition. In the iterative process, by solving the modified homological equations, we ensure that the transformed mapping is still reversible. As an application of the obtained theorem, the boundedness of solutions is investigated for a class of asymmetric oscillators.