Non-smooth saddle-node bifurcations II: Dimensions of strange attractors
Non-smooth saddle-node bifurcations II: Dimensions of strange attractors
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DOI：
10.1017/etds.2017.4
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发表时间：
2014-12
影响因子：
0.9
通讯作者：
G. Fuhrmann;M. Groger;T. Jager
中科院分区：
文献类型：
--
作者：
G. Fuhrmann;M. Groger;T. Jager
研究了拟周期强迫区间映射非光滑鞍节点分岔所产生的奇异非混沌吸引子的几何和拓扑性质。通过将吸引子解释为连续曲线迭代的极限对象并控制后者的几何形状，我们确定了它们的豪斯多夫维和盒计数维，并证明它们取不同的值。此外，同样的方法允许我们描述吸引子的拓扑结构并证明它们的极小性。
We study the geometric and topological properties of strange non-chaotic attractors created in non-smooth saddle-node bifurcations of quasiperiodically forced interval maps. By interpreting the attractors as limit objects of the iterates of a continuous curve and controlling the geometry of the latter, we determine their Hausdorff and box-counting dimension and show that these take distinct values. Moreover, the same approach allows us to describe the topological structure of the attractors and to prove their minimality.