Parabolic carpets

Jonathan Fraser; Natalia Anna Jurga

doi:10.1007/s11856-025-2715-4

Parabolic carpets

Jonathan Fraser, Natalia Anna Jurga^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

Abstract

We introduce and study a family of non-conformal and non-uniformly contracting iterated function systems. We refer to the attractors of such systems as parabolic carpets. Roughly speaking they may be thought of as nonlinear analogues of self-affine carpets which are allowed to have parabolic fixed points. We compute the L^q-spectrum of a class of weak Gibbs measures supported on parabolic carpets as well as the box dimensions of the carpet itself.

Original language	English
Number of pages	39
Journal	Israel Journal of Mathematics
Early online date	20 Jan 2025
DOIs	https://doi.org/10.1007/s11856-025-2715-4
Publication status	E-pub ahead of print - 20 Jan 2025

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10.1007/s11856-025-2715-4Licence: CC BY

Fraser-2025-Parabolic-carpets-IsraelJMath-CCBY
Copyright © 2025, The Author(s). This article is distributed under the terms of the Creative Commons Attribution 4.0 International License, which permits unrestricted use, distribution and reproduction in any medium, provided the appropriate credit is given to the original authors and the source, and a link is provided to the Creative Commons license, indicating if changes were made (https://creativecommons.org/licenses/by/4.0/).
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Fractals, dimension theory: Fractals, dimension theory and random matrix products
Jurga, N. (PI)
The Leverhulme Trust
1/05/22 → 30/04/25
Project: Standard
New perspectives in the dimension: New perspectives in the dimension theory of fractals
Fraser, J. (PI)
The Leverhulme Trust
1/09/19 → 31/01/23
Project: Standard
Fourier analytic techniques: Fourier analytic techniques in geometry and analysis
Fraser, J. (PI) & Falconer, K. (CoI)
EPSRC
1/02/18 → 11/06/21
Project: Standard

Cite this

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title = "Parabolic carpets",

abstract = "We introduce and study a family of non-conformal and non-uniformly contracting iterated function systems. We refer to the attractors of such systems as parabolic carpets. Roughly speaking they may be thought of as nonlinear analogues of self-affine carpets which are allowed to have parabolic fixed points. We compute the Lq-spectrum of a class of weak Gibbs measures supported on parabolic carpets as well as the box dimensions of the carpet itself.",

author = "Jonathan Fraser and Jurga, {Natalia Anna}",

note = "Funding: The authors were both supported by an EPSRC Standard Grant (EP/R015104/1). J. M. Fraser was also supported by a Leverhulme Trust Research Project Grant (RPG-2019-034) and an RSE Sabbatical Research Grant (70249). N. Jurga was also supported by a Leverhulme Trust Early Career Fellowship (ECF-2021-385).",

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N1 - Funding: The authors were both supported by an EPSRC Standard Grant (EP/R015104/1). J. M. Fraser was also supported by a Leverhulme Trust Research Project Grant (RPG-2019-034) and an RSE Sabbatical Research Grant (70249). N. Jurga was also supported by a Leverhulme Trust Early Career Fellowship (ECF-2021-385).

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N2 - We introduce and study a family of non-conformal and non-uniformly contracting iterated function systems. We refer to the attractors of such systems as parabolic carpets. Roughly speaking they may be thought of as nonlinear analogues of self-affine carpets which are allowed to have parabolic fixed points. We compute the Lq-spectrum of a class of weak Gibbs measures supported on parabolic carpets as well as the box dimensions of the carpet itself.

AB - We introduce and study a family of non-conformal and non-uniformly contracting iterated function systems. We refer to the attractors of such systems as parabolic carpets. Roughly speaking they may be thought of as nonlinear analogues of self-affine carpets which are allowed to have parabolic fixed points. We compute the Lq-spectrum of a class of weak Gibbs measures supported on parabolic carpets as well as the box dimensions of the carpet itself.

U2 - 10.1007/s11856-025-2715-4

DO - 10.1007/s11856-025-2715-4

M3 - Article

SN - 0021-2172

JO - Israel Journal of Mathematics

JF - Israel Journal of Mathematics

ER -

Parabolic carpets

Abstract

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Projects

Fractals, dimension theory: Fractals, dimension theory and random matrix products

New perspectives in the dimension: New perspectives in the dimension theory of fractals

Fourier analytic techniques: Fourier analytic techniques in geometry and analysis

Cite this