Shearless bifurcations for two isochronous resonant perturbations
Abstract
In nontwist systems, primary shearless curves act as barriers to chaotic transport. Surprisingly, the onset of secondary shearless curves has been reported in a few twist systems. Meanwhile, we found that, in twist systems, the onset of these secondary shearless curves is a standard process that may appear as control parameters are varied in situations where there is resonant mode coupling. Namely, we analyze these shearless bifurcations in two-harmonic systems for the standard map, the Ullmann map, and for the Walker-Ford Hamiltonian flow. The onset of shearless curves is related to bifurcations of periodic points. Furthermore, depending on the bifurcation, these shearless curves can emerge alone or in pairs, and in some cases, deform into separatrices.
Keywords
Cite
@article{arxiv.2408.10930,
title = {Shearless bifurcations for two isochronous resonant perturbations},
author = {Bruno B. Leal and Matheus J. Lazarotto and Michele Mugnaine and Alfredo M. Ozorio de Almeida and Ricardo L. Viana and Iberê L. Caldas},
journal= {arXiv preprint arXiv:2408.10930},
year = {2024}
}