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

  • Amit Priyadarshi

    Indian Institute of Technology Delhi, New Delhi, India

  • Manuj Verma

    Indian Institute of Technology Delhi, New Delhi, India

  • Saurabh Verma

    Indian Institute of Information Technology Allahabad, Prayagraj, India
Fractal dimensions of fractal transformations and quantization dimensions for bi-Lipschitz mappings cover

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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 measure corresponding to a weighted iterated function system consisting of bi-Lipschitz mappings under the strong open set condition.

Cite this article

Amit Priyadarshi, Manuj Verma, Saurabh Verma, Fractal dimensions of fractal transformations and quantization dimensions for bi-Lipschitz mappings. J. Fractal Geom. (2024), published online first

DOI 10.4171/JFG/157