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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.
|Israel Journal of Mathematics
|Accepted/In press - 9 Nov 2022
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1/05/22 → 30/04/25
1/08/21 → 31/07/22
1/09/19 → 31/01/23