Denjoy-Wolff like set for rational semigroups
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866910836876902400 |
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| author | Chatterjee, Subham Chakraborty, Gorachand Chakra, Tarun Kumar |
| author_facet | Chatterjee, Subham Chakraborty, Gorachand Chakra, Tarun Kumar |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_14292 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Denjoy-Wolff like set for rational semigroups Chatterjee, Subham Chakraborty, Gorachand Chakra, Tarun Kumar Complex Variables 37F10, 30D30, 37F44 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. |
| title | Denjoy-Wolff like set for rational semigroups |
| topic | Complex Variables 37F10, 30D30, 37F44 |
| url | https://arxiv.org/abs/2502.14292 |