Yong Moo Chung ad Kenichiro Yamamoto

Large deviation principle for linear mod 1 transformations

For $0\le α<1$ and $β>2$, we consider a linear mod 1 transformation on a unit interval; $x\mapstoβx+α$ (${\rm mod}\ 1$), and prove that it satisfies the level-2 large deviation principle with the unique measure of maximal entropy. For the proof, we use the density of periodic measures and Hofbauer's Markov Diagram.