Secondary nontwist phenomena in area-preserving maps. (English) Zbl 1319.37054
Summary: 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.{
©2012 American Institute of Physics}
©2012 American Institute of Physics}
MSC:
| 37M20 | Computational methods for bifurcation problems in dynamical systems |
| 37E15 | Combinatorial dynamics (types of periodic orbits) |
| 37J20 | Bifurcation problems for finite-dimensional Hamiltonian and Lagrangian systems |
| 37G15 | Bifurcations of limit cycles and periodic orbits in dynamical systems |
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