A MOSER'S NON-TWIST THEOREM FOR NEARLY INTEGRABLE MAPPINGS WITH SELF-INTERSECTION PROPERTY

In this paper, we consider a family of nearly integrable mappings on annulus, which has self-intersection property and depends on a small parameter. Without any twist condition, we prove that for many sufficiently small parameters the mappings admit an invariant closed curve. Our result is useful for Lagrange stability of Duffing equations.

Automated summary

In this paper, we investigate a family of nearly integrable mappings on an annulus, which have self-intersection property and depend on a small parameter. Despite the absence of a twist condition, we demonstrate that for many sufficiently small parameters, these mappings possess an invariant closed curve. Our findings have implications for the Lagrange stability of Duffing equations.