不动泛系定理的新研究:泛浑沌和泛怪引子

关于浑沌、引子、怪引子等的研究是非线性分析中的重要课题.文1]在泛系方法论的框架下,讨论了这些问题,提出了泛浑沌、泛引子和泛怪引子的概念,这些概念去掉了诸如连续性、紧性等条件,突出反映了一集合上的二元关系的性质.已有的研究结果指出,泛浑沌、泛引子和泛怪引子分别对应于某个特定的泛系算子作用下的不动子集.本文继续文1、2]的工作,探讨了存在这类泛系不动子集的条件以及它们的构造和相互间的联系.

An Approach on Fixed Pansystems Theorems: Panchaos and Strange Panattractor

The investigations about chaos, at tractor and strange at tractor are main subjects in non-linear analysis. Under the framework of pansystems methodology, reference 1] discussed these problems and introduced the concepts of panchaos, panattractor and strange panattractor. These concepts omit ted the condition of continuity, compactness, etc. and put stress on the properties of binary relations on a set. A certain obtained result indicates that panchaos, panattractor and strange panattractor correspond respectively to fixed subsets of certain pansys tems operators. This paper continues the investigation of 1,2], discusses the existence of these pansystems fixed subsets, their construction and interrelations.