论文标题
逻辑图的图是塔
The graph of the logistic map is a tower
论文作者
论文摘要
动态系统的定性行为可以在图中编码。该图的每个节点都是链循环点的等效类别，并且如果使用任意的小扰动，从节点$ a $到节点$ b $的边缘有一个边缘，从A的任何点开始的轨迹可以将其转向B的任何点。在本文中，我们描述了逻辑图的图形。我们的主要结果是该图始终是塔，即有一个边缘连接每个不同的节点。请注意，这些图永远不会包含周期。如果有从节点A到节点B的边缘，则A中某些周期轨道的不稳定歧管包含最终映射到B上的点。对于特殊的参数值，该塔具有无限的许多节点。
The qualitative behavior of a dynamical system can be encoded in a graph. Each node of the graph is an equivalence class of chain-recurrent points and there is an edge from node $A$ to node $B$ if, using arbitrary small perturbations, a trajectory starting from any point of A can be steered to any point of B. In this article we describe the graph of the logistic map. Our main result is that the graph is always a tower, namely there is an edge connecting each pair of distinct nodes. Notice that these graphs never contain cycles. If there is an edge from node A to node B, the unstable manifold of some periodic orbit in A contains points that eventually map onto B. For special parameter values, this tower has infinitely many nodes.
