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Non-expansive directions for ℤ2 actions
Published online by Cambridge University Press: 24 March 2010
Abstract
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.
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- Copyright © Cambridge University Press 2010
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