论文标题
不连续的单数地图和混乱的路线的一维动力学
One-dimensional Dynamics for a Discontinuous Singular Map and the Routes to Chaos
论文作者
论文摘要
我们访问了一个先前提出的不连续的，两参数的概括，对连续的，一个参数logistic映射，并对两个参数和初始点的不同值的行为进行详尽的数值研究。特别是，存在混乱的路线，没有表现出倍增的时间，而周期加倍是逻辑图中混乱的唯一途径。发现具有X = Infinity作为累积点的蜘蛛网的蜘蛛网被发现，每个邻域都包含地图产生的许多点。
We visit a previously proposed discontinuous, two-parameter generalization of the continuous, one-parameter logistic map and present exhaustive numerical studies of the behavior for different values of the two parameters and initial points. In particular, routes to chaos exist that do not exhibit period-doubling whereas period-doubling is the sole route to chaos in the logistic map. Aperiodic maps are found that lead to cobwebs with x = infinity as accumulation points, where every neighborhood contains infinitely many points generated by the map.
