Take the 2-minute tour ×
MathOverflow is a question and answer site for professional mathematicians. It's 100% free, no registration required.

Let $X$ be a strictly ergodic shift space, and $\omega_1$, $\omega_2$ be two different points in $X$. Is there an automorphism $\Psi$ of $X$ such that $\Psi(\omega_1)=\omega_2$? By an automorphism I mean a shift-commuting homeomorphism of $X$. The answer for a general minimal shift space is, I guess, negative as there are minimal shift spaces with two non-isomorphic ergodic measures. But what if $X$ posses only one ergodic measure?

share|improve this question
add comment

1 Answer

up vote 4 down vote accepted

Strict ergodicity does not seem to change much, i.e. the answer is still negative, see the following theorem (W. Bułatek, J. Kwiatkowski, Strictly ergodic Toeplitz flows with positive entropies and trivial centralizers)

The exist a strictly ergodic Toeplitz flows with trivial centralizer.

By a Toeplitz flow we mean a closure of the orbit of a Toeplitz sequence, together with the shift map. Since any block appears on a Toeplitz sequence with some period, it follows that the unique invariant measure has full support, hence minimality.

share|improve this answer
add comment

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.