论文标题
强烈的迭代功能系统和Barnsley-Vince Triangle
Strongly-Fibred Iterated Function Systems and the Barnsley--Vince triangle
论文作者
论文摘要
我们回顾了与非裁定迭代功能系统（IFSS）相关的半剥夺者的理论，并在具体示例上演示了其应用。特别是，我们介绍了由于Lasota和Myjak而存在的半提取器的标准。我们还讨论了Kieninger标准，该标准使我们能够表征半提取器何时强烈。最后，我们考虑了Barnsley和Vince引入的非缩合IF的具体例子。我们找到了该系统的不变度量，使我们能够描述其半提取器。分析此IF的困难源于以下事实：它最终既不是均匀的，也不是平均合同。
We review the theory of semiattractors associated with non-contractive Iterated Function Systems (IFSs) and demonstrate its applications on a concrete example. In particular, we present criteria for the existence of semiattractors due to Lasota and Myjak. We also discuss the Kieninger criterion which allows us to characterise when a semiattractor is strongly-fibred. Finally, we consider a specific example of a non-contractive IFS introduced by Barnsley and Vince. We find an invariant measure for this system which allows us to describe its semiattractor. The difficulty in analysing this IFS stems from the fact that it is neither eventually contractive nor contractive on average.
