Invertible substitutions and Sturmian sequences

Invertible substitutions and Sturmian sequences

It is known on the one hand that a Sturmian sequence can be generated geometrically by the intersections of a straight line with the unit grid in the plane, and on the other hand that fixed points of invertible substitutions are Sturmian. We give a new characterization of invertible substitutions, which allows to determine the straight line which generates the fixed point of a given invertible ...

Bidimensional Sturmian Sequences and Substitutions

Powers in Sturmian sequences

Invertible Substitutions with a Common Periodic Point

We characterize the invertible substitutions over a two-letter alphabet which share a common periodic point (or fixed point). The argument is geometrical.

Initial Powers of Sturmian Sequences

We investigate powers of prefixes in Sturmian sequences. We obtain an explicit formula for ice(ω), the initial critical exponent of a Sturmian sequence ω, defined as the supremum of all real numbers p > 0 for which there exist arbitrary long prefixes of ω of the form u, in terms of its S-adic representation. This formula is based on Ostrowski’s numeration system. We characterize those irrationa...