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A spectral cocycle for substitution systems and translation flows

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arxiv 1802.04783 v4 pith:SSEGXX5G submitted 2018-02-13 math.DS

Alexander I. Bufetov , Boris Solomyak This is my paper · ORCID
classification math.DS
keywords cocycleflowsspectraltranslationsubstitutionsystemscallconstruction
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For substitution systems and translation flows, a new cocycle, which we call {\em 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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Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Twisted Translation Flows and Effective Weak Mixing

    math.DS 2019-08 conditional novelty 8.0 of 10

    For almost all translation flows in every stratum of Abelian differentials, the paper proves power-law bounds on twisted ergodic integrals, Hölder regularity of spectral measures, and effective weak mixing.

  2. Exact renormalisation for patch frequencies in inflation systems

    math.DS 2025-07 conditional novelty 6.0 of 10

    Exact renormalisation equations yield the relative frequency of any patch in a primitive substitution tiling, with transfer to symbolic and other suspension systems.

  3. H\"older regularity for the spectrum of translation flows

    math.DS 2019-08 conditional novelty 5.0 of 10

    Almost every translation flow in every genus has Hölder-regular spectral measures for Lipschitz test functions, proved via a vector Erdős-Kahane argument in the symbolic framework.

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