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A spectral cocycle for substitution systems and translation flows

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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.

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Acknowledgements

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.

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Authors and Affiliations

  1. Centrale Marseille, I2M, UMR, Aix-Marseille Université, CNRS, 7373, Marseille, France

    Alexander I. Bufetov

  2. Steklov Mathematical Institute of Russian Academy of Sciences, Moscow, 119991, Russia

    Alexander I. Bufetov

  3. Institute for Information Transmission Problems, Moscow, 127051, Russia

    Alexander I. Bufetov

  4. Department of Mathematics, Bar-Ilan University, Ramat-Gan, 5290002, Israel

    Boris Solomyak

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  1. Alexander I. Bufetov
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Correspondence to Boris Solomyak.

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Dedicated to Larry Zalcman, with admiration and gratitude

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Bufetov, A.I., Solomyak, B. A spectral cocycle for substitution systems and translation flows. JAMA 141, 165–205 (2020). https://doi.org/10.1007/s11854-020-0127-2

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  • DOI: https://doi.org/10.1007/s11854-020-0127-2

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