Branched manifold is certainly the finest description of the structure of chaotic attractors, characterizing how the unstable periodic orbits are knotted. Many chaotic attractors produced by strongly dissipative systems were thus topologically described. In spite of this, the different possibilities for the branched manifolds which may be constructed from unimodal maps were never exhaustively listed. This is the task of the present work, starting from the folded (Logistic) map, the torn (Lorenz) map, and the less known torn away map introduced by Rössler in 1979. The case of the “reverse” horseshoe map is also discussed.

中文翻译：

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三种单峰图的分支流形

分支歧管无疑是对混沌吸引子结构的最好描述，它描述了不稳定周期轨道是如何打结的。因此，在拓扑上描述了由强耗散系统产生的许多混沌吸引子。尽管如此，从未详尽列出可能由单峰图构造的分支歧管的不同可能性。这是当前工作的任务，从折叠（后勤）地图，撕裂（洛伦兹）地图以及Rössler在1979年引入的鲜为人知的撕裂地图开始。还讨论了“反向”马蹄形地图的情况。 。