关于无界函数产生的稳定周期螺旋、L-迭代和混沌
About Stable Periodic Helixes, L-iteration and Chaos Generated by Unbounded Functions
摘要：
我们认为稳定的周期螺旋作为一个推广的稳定的周期轨道。我们看到，在所研究的迭代函数类中，混沌总是突然出现。因此，我们将研究从混沌到有序的路径，而不是从有序到混沌的路径。我们表明，自相矛盾的是，真正的混沌可能看起来很像秩序，并在尽可能多的迭代步骤，因为一个人可能希望。然后，我们将提出一个广义的映射迭代的想法，并不意味着周期轨道的存在。我们将表明，在严格确定性的背景下，不可预测性，非周期性秩序，敏感的依赖性和混乱是完全不同的概念，我们将试图表明这种差异是由什么。我们还将提出一个非混沌非周期序的例子。
英文摘要：
We consider stable periodic helixes as a generalization of stable periodic orbits. We see that in the studied class of iterated functions Chaos always arise suddenly. Therefore, we shall study the route from chaos to order rather than the route from order to chaos. We show that, paradoxically, genuine Chaos may look as much like Order and during as many iteration steps as one may wish. Then, we shall propose a generalization of the idea of map iteration that do not imply the existence of periodic orbits. We shall show that, within a strictly deterministic context, unpredictability, aperiodic order, sensitive dependence and chaos are completely different concepts and we shall try to show what this difference is made of. We shall also propose an example of non chaotic aperiodic order.
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