Parabolic carpets
Dynamical Systems
2022-02-07 v1 Classical Analysis and ODEs
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.
Cite
@article{arxiv.2202.02066,
title = {Parabolic carpets},
author = {Jonathan M Fraser and Natalia Jurga},
journal= {arXiv preprint arXiv:2202.02066},
year = {2022}
}
Comments
30 pages, 1 figure