Problem 99
(Doug (Lind?)) Find open partitions in $\Sigma _{1/2,1/2}$ that are not weakly Bernoulli. Find invariants of finitary codes.
(Doug (Lind?)) Find open partitions in $\Sigma _{1/2,1/2}$ that are not weakly Bernoulli. Find invariants of finitary codes.
Comments
Perhaps related to [bowen1975smooth] ?
Keane and Smorodinsky showed that two aperiodic shifts of finite type are finitarily isomorphic iff they have the same topological entropy (“The finitary isomorphism theorem for Markov shifts”, Bull. AMS 1 (1979)m 436-438). One consequence is that an ergodic (algebraic) automorphism of the 2-torus has a partition into sets with nonempty interior and bourdary of measure zero that is an independent Bernoulli generator. The reference above to Bowen’s paper shows that in dimension 3 such a partition cannot be smooth.