On the modulus of continuity for spectral measures in substitution dynamics

DOI10.1016/j.aim.2014.04.004zbMath1339.37004arXiv1305.7373OpenAlexW2964130274MaRDI QIDQ2452070

Alexander I. Bufetov, B. M. Solomyak

Publication date: 28 May 2014

Published in: Advances in Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1305.7373

zbMATH Keywords

Diophantine approximationHölder continuityspectral measuresubstitution dynamical systemBernoulli convolution

Mathematics Subject Classification ID

Ergodic theorems, spectral theory, Markov operators (37A30) Symbolic dynamics (37B10) Hausdorff and packing measures (28A78) Flows on surfaces (37E35)

Related Items (26)

Trigonometric series and self-similar sets ⋮ Spectral theory of regular sequences ⋮ On substitution automorphisms with pure singular spectrum ⋮ Fourier decay of self-similar measures and self-similar sets of uniqueness ⋮ Self-similarity and spectral theory: on the spectrum of substitutions ⋮ Logarithmic Fourier decay for self conformal measures ⋮ Quantitative weak mixing for interval exchange transformations ⋮ Self-similar sets and measures on the line ⋮ Uniformly distributed orbits in \(\mathbb{T}^d\) and singular substitution dynamical systems ⋮ The Hölder property for the spectrum of translation flows in genus two ⋮ On ergodic averages for parabolic product flows ⋮ Return words of linear involutions and fundamental groups ⋮ Renormalisation of Pair Correlations and Their Fourier Transforms for Primitive Block Substitutions ⋮ A spectral cocycle for substitution systems and translation flows ⋮ Hölder regularity for the spectrum of translation flows ⋮ Slow chaos in surface flows ⋮ On the exceptional set for absolute continuity of Bernoulli convolutions ⋮ On the Fourier transform of coin-tossing type measures ⋮ Pointwise normality and Fourier decay for self-conformal measures ⋮ Singular substitutions of constant length ⋮ Fourier decay for self-similar measures ⋮ Renormalisation of pair correlation measures for primitive inflation rules and absence of absolutely continuous diffraction ⋮ Corrigendum to: ``Hölder regularity for the spectrum of translation flows ⋮ Seventy years of Salem numbers ⋮ Twisted translation flows and effective weak mixing ⋮ Twisted cohomological equations for translation flows

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