Symmetric Rigidity for Circle Endomorphisms with Bounded Geometry

Abstract

Let $f$ and $g$ be two circle endomorphisms of degree $d\ge 2$ 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.

22 pages, 5 figures

References in corpus (3)

• Asymptotically Affine and Asymptotically Conformal Circle Endomorphisms
• Teichmüller Structures and Dual Geometric Gibbs Type Measure Theory for Continuous Potentials
• Function Models for Teichmüller Spaces and Dual Geometric Gibbs Type Measure Theory for Circle Dynamics