Packing measure and dimension of the limit sets of IFSs of generalized complex continued fractions

Autor:	Inui, Kanji, Sumi, Hiroki
Rok vydání:	2022
Předmět:	Mathematics - Dynamical Systems Mathematics - Complex Variables 28A78 28A80
Druh dokumentu:	Working Paper
Popis:	We consider a family of conformal iterated function systems (for short, CIFSs) of generalized complex continued fractions. Note that in our previous paper we showed that the proper-dimensional Hausdorff measure of the limit set is zero and the packing measure of the limit set with respect to the Hausdorff dimension is positive. In this paper, we show that the packing dimension and the Hausdorff dimension of the limit set of each CIFS in the family are equal, and the proper-dimensional packing measure of the limit set is finite. Comment: arXiv admin note: text overlap with arXiv:1812.07999. To appear in Journal of Difference Equations and Applications, DOI: 10.1080/10236198.2024.2387617
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2204.04460 Zobrazit plný text záznamu View this record from Arxiv