Symmetric rigidity for circle endomorphisms having bounded geometry

Adamski, J.; Hu, Yunchun; Jiang, Yunping; Wang, Zhe

doi:10.1090/proc/15921

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Ced(d) ⊂ Usce(d) ⊂ Uqce(d) ⊂ Bgce(d) ⊂ Ce(d)2

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“…The precise definition of bounded nearby geometry is given and its equivalence to uniform quasisymmetry is proved in [8,9]. For more on circle endomorphisms with bounded geometry and/or bounded nearby geometry, see also [1,5,10,11]).…”

Section: Ced(d) ⊂ Usce(d) ⊂ Uqce(d) ⊂ Bgce(d) ⊂ Ce(d)mentioning

confidence: 99%

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Symmetric Rigidity for Circle Endomorphisms with Bounded Geometry

Adamski,

Hu,

Jiang

et al. 2021

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Let f and g be two circle endomorphisms of degree d ≥ 2 such that each has bounded geometry, preserves the Lebesgue measure, and fixes 1. Let h fixing 1 be the topological conjugacy from f to g. That is, h • f = g • h. We prove that h is a symmetric circle homeomorphism if and only if h = Id. Many other rigidity results in circle dynamics follow from this very general symmetric rigidity result.

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Section: Ced(d) ⊂ Usce(d) ⊂ Uqce(d) ⊂ Bgce(d) ⊂ Ce(d)mentioning

confidence: 99%

“…However, as long as at least one of the maps is not in UQCE(d), the conjugacy h may not be quasisymmetric. Refer to [1,5,7,10,11].…”

Section: Ced(d) ⊂ Usce(d) ⊂ Uqce(d) ⊂ Bgce(d) ⊂ Ce(d)mentioning

confidence: 99%