Journal de l’École polytechnique. Mathématiques

Richard M. Höfer

Christophe Prange

Franck Sueur

Motion of several slender rigid filaments in a Stokes flow

Juhan Aru

Ellen Powell

A characterisation of the continuum Gaussian free field in arbitrary dimensions

Alexander I. Bufetov

Boris Solomyak

Alexander I. Bufetov & Boris Solomyak
Corrigendum to “Hölder regularity for the spectrum of translation flows”
Tome 9 (2022), p. 1513-1514.
https://doi.org/10.5802/jep.212
© Les auteurs, 2022.
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e-ISSN : 2270-518X
Tome 9, 2022, p. 1513–1514 DOI: 10.5802/jep.212
CORRIGENDUM TO
“HÖLDER REGULARITY FOR THE SPECTRUM OF
TRANSLATION FLOWS”
by Alexander I. Bufetov & Boris Solomyak
Abstract. — The paper corrects the formulation of [3, Prop. 5.4], whose proof is unchanged.
Résumé (Correction à “Régularité Hölder pour le spectre des flots de translation” )
Cet article corrige la formulation de [3, Prop. 5.4], dont la preuve est inchangée.
In [3, Prop. 5.4] a different order of quantifiers was needed from the one stated.
The following proposition was, in fact, proven in the paper, and this is the correct
formulation:
Proposition. — For any ε1 > 0 there exist δ0 > 0 and % > 0 such that for P-a.e.
a ∈ Ωq and any δ ∈ (0, δ0), for all B > 1, and every Oseledets subspace HJa corre-
sponding to a, containing the unstable subspace Eua,
dimH(E(%, δ, B) ∩HJa ) 6 dim(HJa )− κ+ ε1,
where κ = dim(Eua).
The short derivation of [3, Th. 4.1] from [3, Prop. 5.4] in this form and the proof of
the proposition do not require any changes.
Incidentally, exactly the same mixed-up parameter dependence is present in
[2, Prop. 9.1], and the correction is also the same. We would like to note that the
proposition with the order of quantifiers as it was published, is, in fact, correct when
the Rauzy induction is periodic; essentially, in the case of a single substitution, as it
was shown in [1].
Acknowledgements. — We are grateful to Rodrigo Treviño who pointed out the mis-
take to us.
Mathematical subject classification (2020). — 37A30, 37B1, 37E35, 28A78.
Keywords. — Translation flows, spectral measures, matrix Riesz products, upper Lyapunov expo-
nents, Erdős-Kahane argument, Bratteli-Vershik automorphisms, renormalization cocycle.
e-ISSN: 2270-518X http://jep.centre-mersenne.org/
1514 A. I. Bufetov & B. Solomyak
References
[1] A. I. Bufetov & B. Solomyak – “On the modulus of continuity for spectral measures in substitution
dynamics”, Adv. Math. 260 (2014), p. 84–129.
[2] , “The Hölder property for the spectrum of translation flows in genus two”, Israel J. Math.
223 (2018), no. 1, p. 205–259.
[3] , “On the modulus of continuity for spectral measures in substitution dynamics”, J. Éc.
polytech. Math. 8 (2021), p. 279–310.
Manuscript received 31st May 2022
accepted 26th September 2022
Alexander I. Bufetov, Aix-Marseille Université, CNRS, Centrale Marseille, I2M, UMR 7373,
39 rue F. Joliot Curie, Marseille, France
Steklov Mathematical Institute of RAS, Moscow, Russia
Institute for Information Transmission Problems, Moscow, Russia
E-mail : bufetov@mi.ras.ru
Boris Solomyak, Department of Mathematics, Bar-Ilan University
Ramat-Gan, Israel
E-mail : bsolom3@gmail.com
Url : https://u.math.biu.ac.il/~solomyb/personal.html
J.É.P. — M., 2022, tome 9


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Motion of several slender rigid filaments in a Stokes flow

A characterisation of the continuum Gaussian free field in arbitrary dimensions

Corrigendum to “Hölder regularity for the spectrum of translation flows”

A rigidity result for metric measure spaces with Euclidean heat kernel

Unconditional Chebyshev biases in number fields

Invariant measures on products and on the space of linear orders

How Lagrangian states evolve into random waves

The trace-reinforced ants process does not find shortest paths

On the Bertini regularity theorem for arithmetic varieties

Quantitative De Giorgi methods in kinetic theory

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