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

2022/12/19 by Manuj Verma, Verma, Manuj, Amit Priyadarshi +3 · 1 citation
Computer Science · Mathematics · #Dynamical Systems (math.DS) #FOS: Mathematics #Image Retrieval and Classification Techniques #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.2212.09669

openalex publication_date 2022/12/19 · openalex created_date 2023/01/04 · openalex updated_date 2026/07/28

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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