摘要
在欧氏空间中,分形的盒计数维数在双Lipschitz变换下是不变的。在此基础上,利用盒计数维数的有限稳定性和管状邻域定理证明了m维紧致光滑流形上的分形的盒计数维数是C1嵌入不变的。
In Eudidean space,Box-counting dimension is invariant under paired Lipschitz transformations.On this basis,it is proved by applying finite stability of Box-counting dimension and tubular neighborhood theorem that the Box-counting dimension of fractal on a compact and smooth manifold is invariant under C 1 embeddings.
出处
《南昌大学学报(理科版)》
CAS
1998年第3期213-215,共3页
Journal of Nanchang University(Natural Science)
关键词
光滑流形
分形
盒计数维数
嵌入不变性
smooth manifold,fractal,Box-counting dimension,C 1 embedding,tubular neighborhood