Bifurcations of families of 1D-tori in 4D symplectic maps.
Bifurcations of families of 1D-tori in 4D symplectic maps.
复制标题
4D 辛图中 1D-tori 族的分叉。
作者：
Franziska Onken;Steffen Lange;R. Ketzmerick;A. Bäcker
具有混合相空间的一般4D辛映射的正则结构由一维椭圆环面的单参数簇组成。这样的族显示出明显的折弯、缝隙和新的分支。我们用跨越共振时的族的分叉来解释这些特征。对于这些分叉，不需要改变外部参数。取而代之的是沿族变化的纵向频率，起分叉参数的作用。作为一个例子，我们通过在三维相空间切片、局部二维投影和频率空间中可视化椭圆和双曲一维环面来研究两个耦合的标准映射。所观察到的分叉与先前得到的准周期强迫振子的解析预测是一致的。此外，从这种分叉中出现的新家族形成了相应的共振通道的骨架。
The regular structures of a generic 4d symplectic map with a mixed phase space are organized by one-parameter families of elliptic 1d-tori. Such families show prominent bends, gaps, and new branches. We explain these features in terms of bifurcations of the families when crossing a resonance. For these bifurcations, no external parameter has to be varied. Instead, the longitudinal frequency, which varies along the family, plays the role of the bifurcation parameter. As an example, we study two coupled standard maps by visualizing the elliptic and hyperbolic 1d-tori in a 3d phase-space slice, local 2d projections, and frequency space. The observed bifurcations are consistent with the analytical predictions previously obtained for quasi-periodically forced oscillators. Moreover, the new families emerging from such a bifurcation form the skeleton of the corresponding resonance channel.
影响因子：
2.4
作者：
Richter, Martin;Lange, Steffen;Ketzmerick, Roland
通讯作者：
Ketzmerick, Roland