Equi-Baire One Families of Möbius Transformations and One-Parameter Subgroups of $\mathrm{PSL}(2,\mathbb{C}$)
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866914368129597440 |
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| author | Dutta, Sandipan Vanlalruatkimi Ramdikpuia, Jonathan |
| author_facet | Dutta, Sandipan Vanlalruatkimi Ramdikpuia, Jonathan |
| contents | We study the Equi-Baire one property families of Möbius transformations on the Riemann sphere. For a loxodromic map $f$, we show its iterates $\{f^n\}$ form an orbitally Equi-Baire one family on the attracting basin. For a one-parameter subgroup $\{f_t \}$, we prove it is Equi-Baire one on all compact sets of $\widehat{\mathbb{C}}$ if and only if the subgroup is relatively compact in $\mathrm{SL}(2,\mathbb{C})$. This provides a dynamical characterization of the Equi-Baire one condition for Möbius families. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_03794 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Equi-Baire One Families of Möbius Transformations and One-Parameter Subgroups of $\mathrm{PSL}(2,\mathbb{C}$) Dutta, Sandipan Vanlalruatkimi Ramdikpuia, Jonathan Dynamical Systems General Topology We study the Equi-Baire one property families of Möbius transformations on the Riemann sphere. For a loxodromic map $f$, we show its iterates $\{f^n\}$ form an orbitally Equi-Baire one family on the attracting basin. For a one-parameter subgroup $\{f_t \}$, we prove it is Equi-Baire one on all compact sets of $\widehat{\mathbb{C}}$ if and only if the subgroup is relatively compact in $\mathrm{SL}(2,\mathbb{C})$. This provides a dynamical characterization of the Equi-Baire one condition for Möbius families. |
| title | Equi-Baire One Families of Möbius Transformations and One-Parameter Subgroups of $\mathrm{PSL}(2,\mathbb{C}$) |
| topic | Dynamical Systems General Topology |
| url | https://arxiv.org/abs/2603.03794 |