Abstract |
Blanchard defined a topological dynamical system to have (topological)
completely positive entropy (TCPE) if every nontrivial (i.e. not a single
point) factor has positive entropy. We can define the related notion of
zero-dimensional topological completely positive entropy (ZTCPE); a system
has ZTCPE if every nontrivial zero-dimensional factor has positive entropy.
It's trivial that these notions are not equivalent, but natural to wonder
whether they are for systems which are themselves zero-dimensional. I'll
discuss some positive and negative results related to this question and
give some open questions.
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