Abstract
for substitution systems and translation flows, a new cocycle, which we call the spectral cocycle, is introduced, whose Lyapunov exponents govern the local dimension of the spectral measure for higher-level cylindrical functions. The construction relies on the symbolic representation of translation flows and the formalism of matrix Riesz products.
| Original language | English |
|---|---|
| Pages (from-to) | 165-205 |
| Number of pages | 41 |
| Journal | Journal d'Analyse Mathematique |
| Volume | 141 |
| Issue number | 1 |
| DOIs | |
| State | Published - Sep 2020 |
Bibliographical note
Publisher Copyright:© 2020, The Hebrew University of Jerusalem.
Funding
We are deeply grateful to the anonymous referee whose comments helped us to improve the presentation. The research of A. Bufetov has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme under grant agreement No. 647133 (ICHAOS). A. Bufetov has also been funded by RFBR grant 18-31-20031. The research of B. Solomyak was supported by the Israel Science Foundation (grants 396/15 and 911/19). We would like to thank the Institut Mittag-Leffler of the Royal Swedish Academy of Sciences, where this work started, for its warm hospitality. Part of this work was done while A. B. was visiting Bar-Ilan University and while B.S. was visiting CIRM Luminy in the framework of the “research in pairs” programme. We are deeply grateful to these institutions for their hospitality.
| Funders | Funder number |
|---|---|
| Institut Mittag-Leffler | |
| Horizon 2020 Framework Programme | 647133 |
| European Commission | |
| Russian Foundation for Basic Research | 18-31-20031 |
| Israel Science Foundation | 396/15, 911/19 |
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