arXiv
Open Access
2021
Minkowski dimension of the boundaries of the lakes of Wada
Zhangchi Chen
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.
Penulis (1)
Z
Zhangchi Chen
Akses Cepat
Informasi Jurnal
- Tahun Terbit
- 2021
- Bahasa
- en
- Sumber Database
- arXiv
- Akses
- Open Access ✓