The partial captivity condition for U(1) extensions of expanding maps on the circle

Yushi Nakano, Masato Tsujii, Jens Wittsten

This paper concerns the compact group extension \[ f:\mathbb{T}^2\to \mathbb{T}^2,\quad f (x,s)= (E(x), s+τ(x)\ \text{mod }1) \] of an expanding map $E:\mathbb{S}^1\to \mathbb{S}^1…