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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Fractal dimensions of continuous piecewise linear iterated function systems
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by R. Dániel Prokaj, Peter Raith and Károly Simon
Proc. Amer. Math. Soc. 151 (2023), 4703-4719
DOI: https://doi.org/10.1090/proc/16430
Published electronically: July 28, 2023

Abstract:

We consider iterated function systems on the real line that consist of continuous, piecewise linear functions. Under a mild separation condition, we show that the Hausdorff and box dimensions of the attractor are equal to the minimum of 1 and the exponent which comes from the most natural system of covers of the attractor.
References
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Bibliographic Information
  • R. Dániel Prokaj
  • Affiliation: Alfréd Rényi Institute of Mathematics, Reáltanoda u. 13-15., 1053 Budapest, Hungary
  • MR Author ID: 1478974
  • ORCID: 0000-0003-3379-7215
  • Email: prokajrd@math.bme.hu
  • Peter Raith
  • Affiliation: Fakultät für Mathematik, Universität Wien, Oskar-Morgenstern-Platz 1, 1090 Wien, Austria
  • MR Author ID: 270666
  • Email: peter.raith@univie.ac.at
  • Károly Simon
  • Affiliation: Department of Stochastics, Institute of Mathematics, Budapest University of Technology and Economics, Müegyetem rkp. 3., 1111 Budapest, Hungary; and ELKH-BME Stochastics Research Group, P.O. Box 91, 1521 Budapest, Hungary
  • MR Author ID: 250279
  • ORCID: 0000-0003-2397-3828
  • Email: simonk@math.bme.hu
  • Received by editor(s): August 4, 2022
  • Received by editor(s) in revised form: January 19, 2023, and January 25, 2023
  • Published electronically: July 28, 2023
  • Additional Notes: The research of the first and third authors was partially supported by National Research, Development and Innovation Office - NKFIH, Project K142169. This work was partially supported by the grant Stiftung Aktion Österich Ungarn 103öu6
  • Communicated by: Katrin Gelfert
  • © Copyright 2023 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 151 (2023), 4703-4719
  • MSC (2020): Primary 28A80; Secondary 37E05
  • DOI: https://doi.org/10.1090/proc/16430
  • MathSciNet review: 4634875