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

Abstract : 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.
Document type :
Preprints, Working Papers, ...
Domain :

https://hal.archives-ouvertes.fr/hal-03435777
Contributor : Konstantin Bogdanov Connect in order to contact the contributor
Submitted on : Thursday, November 18, 2021 - 8:09:17 PM
Last modification on : Friday, November 19, 2021 - 3:49:07 AM

### Identifiers

• HAL Id : hal-03435777, version 1
• ARXIV : 2003.11287

### Citation

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

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