Is the Hausdorff dimension of a set and its image equal under binary coding map?
We prove that the Hausdorff dimension of a set F and the Hausdorff dimension of its image ϕ(F) with respect to the measure μ:=λoϕ−1 are equal under coding map ϕ if μ is Gibbs measure and λ is Lebesque measure.
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| Published in | Chaos, solitons and fractals Vol. 11; no. 7; pp. 1093 - 1096 |
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| Main Author | |
| Format | Journal Article |
| Language | English |
| Published |
Elsevier Ltd
01.06.2000
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| Online Access | Get full text |
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| Summary: | We prove that the Hausdorff dimension of a set F and the Hausdorff dimension of its image ϕ(F) with respect to the measure μ:=λoϕ−1 are equal under coding map ϕ if μ is Gibbs measure and λ is Lebesque measure. |
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| ISSN: | 0960-0779 1873-2887 |
| DOI: | 10.1016/S0960-0779(99)00013-2 |