复二次映射的符号模板迭代
Symbolic template iterations of complex quadratic maps
摘要：
自离散动力学作为一个研究领域出现以来，迭代Logistic映射的轨道行为已经得到了广泛的研究，特别是在复二次族的背景下。然而，很少有人知道的轨道行为，如果地图的变化，随着迭代。我们调查的方式，传统的理论Fatou-Julia可能仍然适用于这种情况下，说明如何迭代模式（符号模板）可以影响拓扑的Julia和Mandelbrot集。我们简要地讨论了这种扩展对遗传和神经编码的各种应用的潜力，因为它调查了如何在复制或学习算法中偶尔或重复发生的错误可能会影响动态结果。
英文摘要：
The behavior of orbits for iterated logistic maps has been widely studied since the dawn of discrete dynamics as a research field, in particular in the context of the complex quadratic family. However, little is is known about orbit behavior if the map changes along with the iterations. We investigate in which ways the traditional theory of Fatou-Julia may still apply in this case, illustrating how the iteration pattern (symbolic template) can affect the topology of the Julia and Mandelbrot sets. We briefly discuss the potential of this extension towards a variety of applications in genetic and neural coding, since it investigates how an occasional or a reoccurring error in a replication or learning algorithm may affect the dynamic outcome.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
