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arXiv · 2101.06870

Symmetric Rigidity for Circle Endomorphisms with Bounded Geometry

John Adamski·Yunchun Hu·Yunping Jiang·Zhe Wang
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Abstract

Let $f$ and $g$ be two circle endomorphisms of degree $d\geq 2$ 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, $h\circ f=g\circ h$. 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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John Adamski, Yunchun Hu, Yunping Jiang, Zhe Wang. 2021-01-18. Symmetric Rigidity for Circle Endomorphisms with Bounded Geometry. https://doi.org/10.1090/proc%2F15921

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