A symmetric Lorenz map is obtained by ‘flipping’ one of the two branches of a symmetric unimodal map. We use this to derive a Sharkovsky-like theorem for symmetric Lorenz maps, and also to find cases where the unimodal map restricted to the critical omega-limit set is conjugate to a Sturmian shift. This has connections with properties of unimodal inverse limit spaces embedded as attractors of some planar homeomorphisms.

中文翻译：

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从单峰映射导出的洛伦兹映射的拓扑特性

对称洛伦兹图是通过“翻转”对称单峰图的两个分支之一来获得的。我们使用它来推导出对称洛伦兹映射的类 Sharkovsky 定理，并且还找到了限制在临界 omega-limit 集的单峰映射与 Sturmian 位移共轭的情况。这与作为一些平面同胚的吸引子嵌入的单峰逆极限空间的性质有关。