TY - JOUR
T1 - Non-expansive directions for ℤ2 actions
AU - Hochman, Michael
PY - 2011/2
Y1 - 2011/2
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=79957480122&partnerID=8YFLogxK
U2 - 10.1017/S0143385709001084
DO - 10.1017/S0143385709001084
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AN - SCOPUS:79957480122
SN - 0143-3857
VL - 31
SP - 91
EP - 112
JO - Ergodic Theory and Dynamical Systems
JF - Ergodic Theory and Dynamical Systems
IS - 1
ER -