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Hausdorff and box dimension of self-affine set in non-Archimedean field by Deng, Yang; Li, Bing; Qiu, Hua is a scholarly article available to read on EtoBox.

What is Hausdorff and box dimension of self-affine set in non-Archimedean field about?

In this paper we consider affine iterated function systems in locally compact non-Archimedean field $\mathbb{F}$. We establish the theory of singular value composition in $\mathbb{F}$ and compute box and Hausdorff dimension of self-affine set in $\mathbb{F}^n$, in generic sense, which is an analogy of Falconer's result for real case. The result has the advantage that no additional assumptions needed to be imposed on the norms of linear parts of affine transformation while such norms are strictly less than $\frac{1}{2}$ for real case, which benefits from the non-Archimedean metric on $\mathbb{F}$.

Author

Deng, Yang; Li, Bing; Qiu, Hua

Published

2022

Language

EN