Non-expansive directions for $Z^2$-actions

Hochman, Michael
Description
We show that any direction in the plane occurs as the unique non-expansive direction of a \mathbb{Z}^{2} action, answering a question of Boyle and Lind. In the case of rational directions, the subaction obtained is non-trivial. We also establish that a cellular automaton can have zero Lyapunov exponents and at the same time act sensitively; and more generally, for any positive real \theta there is a cellular automaton acting on an appropriate subshift with \lambda^{+}=-\lambda^{-}=\theta.
Comment: 24 pages
Keywords
Mathematics - Dynamical Systems, 37B05, 37B10, 37B15