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Autor:
Fraser, Jonathan M., Stuart, Liam
We prove that the Assouad dimension of a parabolic Julia set is $\max\{1,h\}$ where $h$ is the Hausdorff dimension of the Julia set. Since $h$ may be strictly less than 1, this provides examples where the Assouad and Hausdorff dimension are distinct.
Externí odkaz:
http://arxiv.org/abs/2203.04943
Conditions are given which imply that certain non-autonomous analytic iterated function systems (NIFS's) in the complex plane have uniformly perfect attractor sets, while other conditions imply the attractor is pointwise thin, and thus hereditarily n
Externí odkaz:
http://arxiv.org/abs/1912.11534
Conditions are given which imply that certain non-autonomous analytic iterated function systems (NIFS's) in the complex plane have uniformly perfect attractor sets, while other conditions imply the attractor is pointwise thin, and thus hereditarily n
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::4e3de6bd7d1d27fab553cc62899788b3