Complete orbits for twist maps on the plane

Abstract

AbstractTwist maps (θ1,r1)=f(θ,r) are considered in this paper, with no assumption on the periodicity of the map in θ. Under appropriate assumptions, the existence of infinitely many bounded (in r) complete orbits is proven. In particular, our results apply to the class of maps where λ>0 and no arithmetic condition has to be imposed on ω1/ω2.