Rank one Z^d actions and directional entropy

Details Rank one Z^d actions and directional entropy Rank one Z^d actions and directional entropy

2008-09-09

arxiv.org/abs/0809.1626v2

Mathematics

Dynamical Systems

Scientific paper

We study the directional entropy of rank one Z^d actions. We show that if the
sequence of towers generating the action are rectangular in shape, then there
is always a direction along which the directional entropy is zero. If the
rectangles satisfy a "sub-exponential growth" condition, then we show that the
directional entropy is zero in every direction.

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