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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从单峰图导出的洛伦兹图的拓扑性质

对称的Lorenz映射是通过“翻转”对称单峰映射的两个分支之一获得的。我们使用它为对称的Lorenz映射推导类似Sharkovsky的定理，并找到限制在关键欧米伽极限集上的单峰映射与Sturmian位移共轭的情况。这与嵌入为某些平面同胚的吸引子的单峰逆极限空间的性质有关。