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

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 θthere is a cellular automaton acting on an appropriate subshift with λ^{+}=-λ^{-}=θ.

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