论文标题
随机过程的模块化混乱
Modular chaos for random processes
论文作者
论文摘要
在本文中，考虑了符号动力学的基本概括。我们应用了抽象自相似集的概念和混乱引入的相似性图，该轨道在无限的许多模块之间扩展了轨道。动力学不含维度，度量和拓扑假设。它将所有三种类型的Poincare，Li-Yorke和Devaney混乱都团结在一起，可以无限制。该研究表明，庞加雷混乱的动态是分析离散和连续时间随机过程的非凡用途。示例说明结果。
In the present paper, an essential generalization of the symbolic dynamics is considered. We apply the notions of abstract self-similar sets and the similarity map for a chaos introduction, which orbits are expanded among infinitely many modules. The dynamics is free of dimensional, metrical and topological assumptions. It unites all the three types of Poincare, Li-Yorke and Devaney chaos in a single model, which can be unbounded. The research demonstrates that the dynamics of Poincare chaos is of exceptional use to analyze discrete and continuous-time random processes. Examples, illustrating the results are provided.
