Rotation number of interval contracted rotations

Michel Laurent, Arnaldo Nogueira

Let $0<\lambda <1$. We consider the one-parameter family of circle $\lambda$-affine contractions $f_{\delta }:x\in [0,1)\mapsto \lambda x+\delta \mathrm{mod}1$, where $0\le \delta <1$. Let $\rho$ be the rotation num…