Quantitative weak mixing for typical Salem substitution suspension flows
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , |
|---|---|
| Format: | Preprint |
| Publié: |
2026
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866909996879446016 |
|---|---|
| author | Marshall-Maldonado, Juan Solomyak, Boris |
| author_facet | Marshall-Maldonado, Juan Solomyak, Boris |
| contents | The paper investigates quantitative weak mixing of Salem substitutions flows. We prove that for a substitution whose substitution matrix is irreducible over the rationals and the dominant eigenvalue is a Salem number, for almost every suspension flow with a piecewise constant roof function, quantitative weak mixing holds with a rate that is slightly worse than a power of $\log\log$. We do not know if this is sharp, but we do show that for any suspension flow of this kind, quantitative weak mixing with a polynomial rate is impossible. Results for specific systems are often much weaker than for ``typical'' or ``generic'' ones. In the Appendix we explain how a minor modification of an argument from Bufetov and Solomyak (2014) yields very weak, but nevertheless quantitative weak mixing estimates of $\log^*$ type for the {\em self-similar} suspension flow over a Salem substitution. Simultaneously this provides first quantitative decay rates for the Fourier transform of Salem Bernoulli convolutions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_15035 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Quantitative weak mixing for typical Salem substitution suspension flows Marshall-Maldonado, Juan Solomyak, Boris Dynamical Systems 11K16, 37A30, 37B10, 47A11 The paper investigates quantitative weak mixing of Salem substitutions flows. We prove that for a substitution whose substitution matrix is irreducible over the rationals and the dominant eigenvalue is a Salem number, for almost every suspension flow with a piecewise constant roof function, quantitative weak mixing holds with a rate that is slightly worse than a power of $\log\log$. We do not know if this is sharp, but we do show that for any suspension flow of this kind, quantitative weak mixing with a polynomial rate is impossible. Results for specific systems are often much weaker than for ``typical'' or ``generic'' ones. In the Appendix we explain how a minor modification of an argument from Bufetov and Solomyak (2014) yields very weak, but nevertheless quantitative weak mixing estimates of $\log^*$ type for the {\em self-similar} suspension flow over a Salem substitution. Simultaneously this provides first quantitative decay rates for the Fourier transform of Salem Bernoulli convolutions. |
| title | Quantitative weak mixing for typical Salem substitution suspension flows |
| topic | Dynamical Systems 11K16, 37A30, 37B10, 47A11 |
| url | https://arxiv.org/abs/2601.15035 |