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Non-expansive directions for ℤ2 actions

Published online by Cambridge University Press:  24 March 2010

MICHAEL HOCHMAN
MICHAEL HOCHMAN*
Affiliation:
Department of Mathematics, Princeton University, Princeton, NJ 08544, USA (email: [email protected])
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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.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 31 , Issue 1 , February 2011 , pp. 91 - 112
Copyright
Copyright © Cambridge University Press 2010

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