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arXiv · 0906.0609

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

Michael Hochman
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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 \theta there is a cellular automaton acting on an appropriate subshift with \lambda^{+}=-\lambda^{-}=\theta.

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Michael Hochman. 2009-06-02. Non-expansive directions for $Z^2$-actions. https://doi.org/10.1017/s0143385709001084

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