Substitutions and Möbius disjointness

Sébastien Ferenczi (1) , Joanna Kułaga-Przymus (2, 3) , Mariusz Lemańczyk (3) , Christian Mauduit (1)

1 I2M - Institut de Mathématiques de Marseille
2 Institute of Mathematics, Polish Academy of Sciences, Poland
3 Faculty of Mathematics and Computer Science

We show that Sarnak's conjecture on Möbius disjointness holds for all subshifts given by bijective substitutions and some other similar dynamical systems, e.g.\ those generated by Rudin-Shapiro type sequences.

Mots clés: bijective substitutions; Möbius disjointness; Rudin-Shapiro type sequences; spectral theory; odometers; Morse cocycles; Toeplitz extensions; Sarnak’s conjecture

Domaines: Systèmes dynamiques [math.DS]; Théorie des nombres [math.NT]

Sébastien Ferenczi, Joanna Kułaga-Przymus, Mariusz Lemańczyk, Christian Mauduit. Substitutions and Möbius disjointness. 2016. ⟨hal-01297978⟩