arXiv Open Access 2021

Minkowski dimension of the boundaries of the lakes of Wada

Zhangchi Chen
Lihat Sumber

Abstrak

The lakes of Wada are three disjoint simply connected domains in $S^2$ with the counterintuitive property that they all have the same boundary. The common boundary is a indecomposable continuum. In this article we calculated the Minkowski dimension of such boundaries. The lakes constructed in the standard Cantor way has $\ln(6)/\ln(3)\approx 1.6309$-dimensional boundary, while in general, for any number in $[1,2]$ we can construct lakes with such dimensional boundaries.

Topik & Kata Kunci

Penulis (1)

Z

Zhangchi Chen

Format Sitasi

Chen, Z. (2021). Minkowski dimension of the boundaries of the lakes of Wada. https://arxiv.org/abs/2107.05626

Akses Cepat

Lihat di Sumber
Informasi Jurnal
Tahun Terbit
2021
Bahasa
en
Sumber Database
arXiv
Akses
Open Access ✓