Markoff-Lagrange spectrum of one-sided shifts (Q6581853)

The authors determine the smallest accumulation point of binary sequences that are maximal in their shift orbits. This problem is trivial for the lexicographic order. They show that its solution is the fixed point of a substitution for the alternating lexicographic order. For orders defined by cylinders, they show that the solutions are \(S\)-adic sequences, where \(S\) is a certain infinite set of substitutions that contains Sturmian morphisms. They also consider a similar problem for symmetric ternary shifts, which is applicable to the multiplicative version of the Markoff-Lagrange spectrum.