Quantization of Cantor-Like Set on the Real Projective Line
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866913372971204608 |
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| author | Hossain, A. Banerjee, A. Akhtar, Md. N. |
| author_facet | Hossain, A. Banerjee, A. Akhtar, Md. N. |
| contents | In this article, an iterated function system (IFS) is considered on the real projective line $\mathbb{RP}^1$ so that the attractor is a Cantor-like set. Hausdorff dimension of this attractor is estimated. The existence of a probability measure associated with this IFS on $\mathbb{RP}^1$ is also demonstrated. It is shown that the $n$-th quantization error of order $r$ for the push-forward measure is a constant multiple of the $n$-th quantization error of order $r$ of the original measure. Finally, an upper bound for the $n$-th quantization error of order $2$ for this measure is provided. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_09954 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Quantization of Cantor-Like Set on the Real Projective Line Hossain, A. Banerjee, A. Akhtar, Md. N. Dynamical Systems 28A80, 37A50 In this article, an iterated function system (IFS) is considered on the real projective line $\mathbb{RP}^1$ so that the attractor is a Cantor-like set. Hausdorff dimension of this attractor is estimated. The existence of a probability measure associated with this IFS on $\mathbb{RP}^1$ is also demonstrated. It is shown that the $n$-th quantization error of order $r$ for the push-forward measure is a constant multiple of the $n$-th quantization error of order $r$ of the original measure. Finally, an upper bound for the $n$-th quantization error of order $2$ for this measure is provided. |
| title | Quantization of Cantor-Like Set on the Real Projective Line |
| topic | Dynamical Systems 28A80, 37A50 |
| url | https://arxiv.org/abs/2405.09954 |