Denjoy-Wolff like set for rational semigroups
Complex Variables
2025-02-21 v1
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.
Cite
@article{arxiv.2502.14292,
title = {Denjoy-Wolff like set for rational semigroups},
author = {Subham Chatterjee and Gorachand Chakraborty and Tarun Kumar Chakra},
journal= {arXiv preprint arXiv:2502.14292},
year = {2025}
}
Comments
11 pages