On singular substitution ${\mathbb Z}$-actions

Alexander I. Bufetov (1, 2, 3) , Boris Solomyak

1 CNRS - Centre National de la Recherche Scientifique
2 I2M - Institut de Mathématiques de Marseille
3 AMU - Aix Marseille Université

We obtain a sufficient condition for a substitution ${\mathbb Z}$-action to have pure singular spectrum in terms of the top Lyapunov exponent of the spectral cocycle introduced in arXiv:1802.04783 by the authors. It is applied to a family of examples, including those associated with self-similar interval exchange transformations.

Domaines: Mathématiques [math]

Alexander I. Bufetov, Boris Solomyak. On singular substitution ${\mathbb Z}$-actions. 2021. ⟨hal-03435777⟩