Non-smooth saddle-node bifurcations I: existence of an SNA
Non-smooth saddle-node bifurcations I: existence of an SNA
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DOI：
10.1017/etds.2014.92
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发表时间：
2014-12
影响因子：
0.9
通讯作者：
G. Fuhrmann
中科院分区：
文献类型：
--
作者：
G. Fuhrmann
研究了拟周期强迫单调区间映射族，给出了相应系统存在非一致双曲吸引子的参数存在的充分条件。这相当于存在汇源轨道，即在时间上向前和向后都具有正Lyapunov指数的轨道。吸引子本身是一个具有负Lyapunov指数的非连续不变图，通常被称为SNA。与以前在这个方向上的结果不同，我们的条件是纤维映射中的${\mathcal{C}}^{2}$-开放。应用关于斜积中鞍点分支的一个一般结果，我们得到了在各自的族中出现非光滑分支的结论。明确的例子说明了派生语句的适用性。
We study one-parameter families of quasi-periodically forced monotone interval maps and provide sufficient conditions for the existence of a parameter at which the respective system possesses a non-uniformly hyperbolic attractor. This is equivalent to the existence of a sink-source orbit, that is, an orbit with positive Lyapunov exponent both forwards and backwards in time. The attractor itself is a non-continuous invariant graph with negative Lyapunov exponent, often referred to as ‘SNA’. In contrast to former results in this direction, our conditions are ${\mathcal{C}}^{2}$-open in the fibre maps. By applying a general result about saddle-node bifurcations in skew-products, we obtain a conclusion on the occurrence of non-smooth bifurcations in the respective families. Explicit examples show the applicability of the derived statements.