Secondary shearless bifurcations for two isochronous resonant perturbations.

Abstract

Shearless curves are characteristic of nontwist systems and are not expected to exist in twist systems. However, the appearance of secondary shearless curves in the central area of islands has been reported in a few studies where the twist condition is still satisfied. In addition to these studies, we present a scenario in which secondary shearless curves emerge when two independent resonances interact on the same resonant surface. By varying the magnitude of the perturbation parameters, we observe the emergence of multiple secondary shearless curves, which can appear in pairs or individually. Our results are obtained for two discrete systems-the two-harmonic standard map and the Ullmann map-as well as for the Walker-Ford Hamiltonian flow.