Abstract
Let \(\text {Homeo}_{+}(\mathbb {S}^1)\) denote the group of orientation preserving homeomorphisms of the circle \(\mathbb {S}^1\). A subgroup G of \(\text {Homeo}_{+}(\mathbb {S}^1)\) is tightly transitive if it is topologically transitive and no subgroup H of G with \([G: H]=\infty \) has this property; is almost minimal if it has at most countably many nontransitive points. In the paper, we determine all the topological conjugation classes of tightly transitive and almost minimal subgroups of \(\text {Homeo}_{+}(\mathbb {S}^1)\) which are isomorphic to \(\mathbb {Z}^n\) for any integer \(n\ge 2\).
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This work is supported by NSFC (Nos. 11771318, 11790274).
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Xu, H., Shi, E. Topological Conjugation Classes of Tightly Transitive Subgroups of \(\text {Homeo}_{+}(\mathbb {S}^1)\). J Dyn Diff Equat 34, 1049–1066 (2022). https://doi.org/10.1007/s10884-020-09912-w
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DOI: https://doi.org/10.1007/s10884-020-09912-w