Hausdorff and box dimensions of self-affine sets in a locally compact non-Archimedean field

作者：Deng, Yang; Li, Bing; Qiu, Hua^*

来源：Nonlinearity, 2023, 36(7): 3483-3500.

DOI：10.1088/1361-6544/acd515

• non-Archimedean field
• Hausdorff dimension
• self-affine set
• singular value decomposition

We consider affine iterated function systems in a locally compact nonArchimedean field F. We establish the theory of singular value decomposition in F and compute the box and Hausdorff dimensions of self-affine sets in F-n, in generic sense, which is an analogy of Falconer's result for the real case. In R-n, the box and Hausdorff dimensions of self-affine sets can be obtained only when the norms of linear parts of affine transformations are strictly less than 1/2 . However, in a locally compact non-Archimedean field, the same result can be obtained without the restriction of the norms.

• 单位
  南京大学