Non-expansive directions for ℤ² actions

We show that any direction in the plane occurs as the unique non-expansive direction of a ℤ² 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 acting on a subshift can have zero Lyapunov exponents and at the same time act sensitively; and, more generally, for any positive real θ there is a cellular automaton acting on an appropriate subshift with λ⁺= -λ^-=θ.