盒计数维数的嵌入不变性

THE INVARIANCE OF BOX-COUNTING DIMENSION UNDER EMBEDDINGS

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.