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arXiv · 2202.02066

Parabolic carpets

Jonathan M Fraser·Natalia Jurga
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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.

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Jonathan M Fraser, Natalia Jurga. 2022-02-04. Parabolic carpets. https://arxiv.org/abs/2202.02066

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