The γ-Dimension of Images of Bi-Lipschitz Function

The integral staircase function defined on a fractal set is special case of the bi-Lipschitz function of order α ∈ (0, 1) and the image of this function does not preserve γ -dimensions. In this paper, we show the sufficient condition for any function defined on a fractal set satisfies the bi-Lipschi...

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Bibliographic Details
Published in:Journal of physics. Conference series 2019-08, Vol.1306 (1), p.12040
Main Authors: Wibowo, S, Kurniawan, V Y, Siswanto
Format: Article
Language:English
Subjects:
Fractals
Lipschitz condition
Physics
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Summary:The integral staircase function defined on a fractal set is special case of the bi-Lipschitz function of order α ∈ (0, 1) and the image of this function does not preserve γ -dimensions. In this paper, we show the sufficient condition for any function defined on a fractal set satisfies the bi-Lipschitz condition of order α ∈ (0, 1). Moreover, the image of the bi-Lipschitz function does not preserve γ -dimensions of its domain.
ISSN:1742-6588
1742-6596
DOI:10.1088/1742-6596/1306/1/012040