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

Abstract

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.

24 pages

References in corpus (1)

• On a zero speed sensitive cellular automaton

Cited by in corpus (2)

• Asymptotic structure in substitution tiling spaces
• Polygonal ${\mathbb{Z}}^2$-subshifts