Instituto de Física, Universidade de São Paulo, São Paulo, 05315-970 São Paulo, Brazil.
Chaos. 2012 Sep;22(3):033142. doi: 10.1063/1.4750040.
Phenomena as reconnection scenarios, periodic-orbit collisions, and primary shearless tori have been recognized as features of nontwist maps. Recently, these phenomena and secondary shearless tori were analytically predicted for generic maps in the neighborhood of the tripling bifurcation of an elliptic fixed point. In this paper, we apply a numerical procedure to find internal rotation number profiles that highlight the creation of periodic orbits within islands of stability by a saddle-center bifurcation that emerges out a secondary shearless torus. In addition to the analytical predictions, our numerical procedure applied to the twist and nontwist standard maps reveals that the atypical secondary shearless torus occurs not only near a tripling bifurcation of the fixed point but also near a quadrupling bifurcation.
现象如重联场景、周期性轨道碰撞和主要无剪切环，已被认为是非扭 maps 的特征。最近，这些现象和二次无剪切环已被分析预测到，在一个椭圆固定点的三倍分叉附近的通用 maps 中。在本文中，我们应用数值方法来寻找内部旋转数分布，这些分布突出了由一个在二次无剪切环中出现的鞍中心分岔引起的稳定性岛屿中周期性轨道的形成。除了分析预测，我们应用于扭和非扭标准 maps 的数值方法揭示了非典型的二次无剪切环不仅出现在固定点的三倍分叉附近，也出现在四倍分叉附近。
