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arXiv · 2502.14292

Denjoy-Wolff like set for rational semigroups

Subham Chatterjee·Gorachand Chakraborty·Tarun Kumar Chakra
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Abstract

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 Denjoy-Wolff like set for this class. We use the concept of Denjoy-Wolff like set to classify the class into 3 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.

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Subham Chatterjee, Gorachand Chakraborty, Tarun Kumar Chakra. 2025-02-20. Denjoy-Wolff like set for rational semigroups. https://arxiv.org/abs/2502.14292

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