Packing measure and dimension of the limit sets of IFSs of generalized complex continued fractions
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arXiv
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| Format: | Preprint |
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2022
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| _version_ | 1866914916929110016 |
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| author | Inui, Kanji Sumi, Hiroki |
| author_facet | Inui, Kanji Sumi, Hiroki |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2204_04460 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Packing measure and dimension of the limit sets of IFSs of generalized complex continued fractions Inui, Kanji Sumi, Hiroki Dynamical Systems Complex Variables 28A78, 28A80 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. |
| title | Packing measure and dimension of the limit sets of IFSs of generalized complex continued fractions |
| topic | Dynamical Systems Complex Variables 28A78, 28A80 |
| url | https://arxiv.org/abs/2204.04460 |