In this paper, a family of quasiperiodically forced piecewise linear maps is considered. It is proved that there exists a unique strange nonchaotic attractor for some set of parameter values. It is the graph of an upper semi-continuous function, which is invariant, discontinuous almost everywhere and attracts almost all orbits. Moreover, both Lyapunov exponents on the attractor is nonpositive. Finally, to demonstrate and validate our theoretical results, numerical simulations are presented to exhibit the corresponding phase portrait and Lyapunov exponents portrait.

中文翻译：

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来自准周期强制分段线性映射族的奇异非混沌吸引子

在本文中，考虑了一系列准周期强制分段线性映射。证明了对于某组参数值存在唯一奇异的非混沌吸引子。它是一个上半连续函数的图，它是不变的，几乎处处不连续，并且吸引了几乎所有的轨道。此外，吸引子上的两个 Lyapunov 指数都是非正的。最后，为了证明和验证我们的理论结果，提出了数值模拟来展示相应的相图和 Lyapunov 指数图。