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<p>In this paper, we introduce the concept of Denjoy-Wolff set in rational semigroups. We show that for finitely generated Abelian rational semigroups, the Denjoy-Wolff like set is countable. Some results concerning the Denjoy-Wolff like set and the Julia set are also discussed. Then we consider a special class of rational semigroups and discuss various properties of the Denjoy-Wolff like set for this class. We use the concept of Denjoy-Wolff like set to classify the class into three sub-classes. We also show that for any semigroup in this class, the semigroup can be partitioned into <i>k</i> partitions where <i>k</i> is the cardinality of the Denjoy-Wolff like set.</p>

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Denjoy-Wolff like set for rational semigroups

  • 期刊论文

  • 发表日期：

    2025年9月2日

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  • Subham Chatterjee,
  • Gorachand Chakraborty,
  • Tarun Kumar Chakra

摘要

In this paper, we introduce the concept of Denjoy-Wolff set in rational semigroups. We show that for finitely generated Abelian rational semigroups, the Denjoy-Wolff like set is countable. Some results concerning the Denjoy-Wolff like set and the Julia set are also discussed. Then we consider a special class of rational semigroups and discuss various properties of the Denjoy-Wolff like set for this class. We use the concept of Denjoy-Wolff like set to classify the class into three sub-classes. We also show that for any semigroup in this class, the semigroup can be partitioned into k partitions where k is the cardinality of the Denjoy-Wolff like set.