Parabolic carpets
Jonathan M Fraser, Natalia Jurga

TL;DR
This paper introduces parabolic carpets, a new class of fractals generated by non-conformal, non-uniformly contracting iterated function systems, and analyzes their measure spectra and dimensions.
Contribution
It defines and studies parabolic carpets, extending self-affine carpets to include systems with parabolic fixed points, and computes their measure spectra and box dimensions.
Findings
Computed the $L^q$-spectrum of weak Gibbs measures on parabolic carpets.
Determined the box dimensions of the parabolic carpets.
Extended the theory of self-affine carpets to non-conformal, parabolic cases.
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 -spectrum of a class of weak Gibbs measures supported on parabolic carpets as well as the box dimensions of the carpet itself.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsMathematical Dynamics and Fractals
