In this paper we investigate iterative roots of strictly monotone upper semi-continuous multifunctions having finitely many jumps. Known results are concerning roots of order 2 for multifunctions of exact one jump. For the general investigation, we introduce a concept `intensity' to formulate the growth of jumps under iteration and find a class of strictly monotone and upper semi-continuous multifunctions of intensity 1, called exclusive multifunctions, each of which has an absorbing interval. Then we use the absorbing interval to construct iterative roots of order $n$ for those exclusive multifunctions.

中文翻译：

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独占多功能的迭代根

在本文中，我们研究了具有有限多次跳跃的严格单调上半连续多功能的迭代根。已知的结果是关于精确一次跳跃的多功能函数的 2 阶根。对于一般研究，我们引入了一个概念“强度”来表述迭代下跳跃的增长，并找到一类强度为 1 的严格单调和上半连续的多重函数，称为互斥多重函数，每个函数都有一个吸收区间。然后我们使用吸收区间为那些互斥的多功能构造$n$阶的迭代根。