R<sup>n</sup>的分形曲线的维数迹

缪克英. Rⁿ的分形曲线的维数迹[J]. 北京工业大学学报, 1996, 22(2): 68-71.

引用本文:

缪克英. Rⁿ的分形曲线的维数迹[J]. 北京工业大学学报, 1996, 22(2): 68-71.

Miao Keying. Dimension Print of Fractal Curve in Rⁿ[J]. Journal of Beijing University of Technology, 1996, 22(2): 68-71.

Citation:

Miao Keying. Dimension Print of Fractal Curve in Rⁿ[J]. Journal of Beijing University of Technology, 1996, 22(2): 68-71.

Rⁿ的分形曲线的维数迹

摘要: 证明了:若T是R的s维良好定义的子集f:R→Rⁿ,f(t)=(t,t²,…,tⁿ),则T在f下的象的维数迹为P(f(T))=R(1/s,2/s,…,n/s).

Abstract: In this paper, the following theorem is proved:let T be a Borel set in R of well-determined dimension s, f:R→Rⁿ, f(t)=(t, t²,……, tⁿ),then the dimension print of the images of T under f is P(f(T))=R(1/s,2/s, ……, n/s).

用微信扫码二维码

分享至好友和朋友圈