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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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Assouad dimension of planar self-affine sets
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by Balázs Bárány, Antti Käenmäki and Eino Rossi PDF
Trans. Amer. Math. Soc. 374 (2021), 1297-1326 Request permission


We calculate the Assouad dimension of a planar self-affine set $X$ satisfying the strong separation condition and the projection condition and show that $X$ is minimal for the conformal Assouad dimension. Furthermore, we see that such a self-affine set $X$ adheres to very strong tangential regularity by showing that any two points of $X$, which are generic with respect to a self-affine measure having simple Lyapunov spectrum, share the same collection of tangent sets.
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Additional Information
  • Balázs Bárány
  • Affiliation: Department of Stochastics, MTA-BME Stochastics Research Group, Budapest University of Technology and Economics, P.O. Box 91, 1521 Budapest, Hungary
  • MR Author ID: 890989
  • Email:
  • Antti Käenmäki
  • Affiliation: Department of Physics and Mathematics, University of Eastern Finland, P.O. Box 111, FI-80101 Joensuu, Finland
  • Email:
  • Eino Rossi
  • Affiliation: Department of Mathematics and Statistics, P.O. Box 68 (Pietari Kalmin katu 5), FI-00014 University of Helsinki, Finland
  • MR Author ID: 1050675
  • Email:
  • Received by editor(s): June 26, 2019
  • Received by editor(s) in revised form: March 5, 2020, and June 19, 2020
  • Published electronically: November 12, 2020
  • Additional Notes: The first author acknowledges support from the grants OTKA K123782, NKFI PD123970, the János Bolyai Research Scholarship of the Hungarian Academy of Sciences. The second author thanks the Academy of Finland (project no. 286877) for financial support. The third author was funded by the University of Helsinki via the project “Quantitative rectifiability of sets and measures in Euclidean spaces and Heisenberg groups” (project no. 7516125).
  • © Copyright 2020 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 374 (2021), 1297-1326
  • MSC (2010): Primary 28A80; Secondary 37C45, 37L30
  • DOI:
  • MathSciNet review: 4196394