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Mathematics > Dynamical Systems

arXiv:2202.02066 (math)
[Submitted on 4 Feb 2022]

Title:Parabolic carpets

Authors: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.
Comments: 30 pages, 1 figure
Subjects: Dynamical Systems (math.DS); Classical Analysis and ODEs (math.CA)
Cite as: arXiv:2202.02066 [math.DS]
  (or arXiv:2202.02066v1 [math.DS] for this version)
  https://doi.org/10.48550/arXiv.2202.02066

Submission history

From: Natalia Jurga [view email]
[v1] Fri, 4 Feb 2022 10:38:51 UTC (88 KB)
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