# Open problems in symbolic dynamics

I would like to know which are some noticeable open problems in symbolic dynamics, including substitution dynamics. I'm especially interested in connections with topological chaos of various forms. Thanks!

• "noticeable": Maybe you meant "noteworthy"? Sep 30, 2021 at 17:32
• or maybe "notable". Oct 1, 2021 at 7:42

The conjecture is known to be true for all two-letter substitutions, but probably the most interesting case that has been solved is by Barge, where he solved the conjecture for all `$$\beta$$-substitutions' - https://arxiv.org/abs/1505.04408