关于Hutchinson算子的连续性
On the continuity of the Hutchinson operator
摘要：
研究了迭代函数系统（IFS）中的Hutchinson算子是否连续。它澄清了分散在最近的文献中的几个部分结果。虽然具有严格吸引子的IFS的主要例子是由压缩族（所谓的双曲系统）提供的，但重点是确保在诱导哈钦森算子时保持各种类似压缩性的条件，除非最近发现严格吸引子经常存在于一大类非压缩映射，即投射映射。这为研究函数的一般连续性是否保证诱导Hutchinson算子的连续性提供了重要的动力。
英文摘要：
We investigate whether the Hutchinson operator associated with the iterated function system (IFS) is continuous. It clarifies several partial results scattered across recent literature. While the main example for IFS with strict attractor was provided by the family of contractions (the so-called hyperbolic system), the accent was put on ensuring that various contractivity-like conditions are preserved when the Hutchinson operator is induced, unless very recently it was discovered that strict attractors are quite often present for a large class of noncontractive maps, namely projective maps. This sets substantial motivation for the study whether in general continuity of functions guarantees continuity of the induced Hutchinson operator.
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