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<p>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 <i>parabolic carpets</i>. 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 <i>L</i><sup><i>q</i></sup>-spectrum of a class of weak Gibbs measures supported on parabolic carpets as well as the box dimensions of the carpet itself.</p>

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Parabolic carpets

  • 期刊论文

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  • 发表日期：

    2025年1月20日

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  • Jonathan M. Fraser,
  • Natalia Jurga

摘要

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.