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arXiv · 2212.09669

Fractal dimensions of fractal transformations and Quantization dimensions for bi-Lipschitz mappings

Manuj Verma·Amit Priyadarshi·Saurabh Verma
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Abstract

In this paper, we study the fractal dimension of the graph of a fractal transformation and also determine the quantization dimension of a probability measure supported on the graph of the fractal transformation. Moreover, we estimate the quantization dimension of the invariant measures corresponding to a weighted iterated function system consisting of bi-Lipschitz mappings under the strong open set condition.

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Manuj Verma, Amit Priyadarshi, Saurabh Verma. 2022-12-19. Fractal dimensions of fractal transformations and Quantization dimensions for bi-Lipschitz mappings. https://arxiv.org/abs/2212.09669

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