Exact packing measure of linear Cantor sets
Exact packing measure of linear Cantor sets
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DOI：
10.1002/mana.200310006
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发表时间：
2003-01
影响因子：
1
通讯作者：
De-Jun Feng
中科院分区：
文献类型：
--
作者：
De-Jun Feng
Let K be the attractor of a linear iterated function system Sjx = ρjx +bj (j = 1, …, m) on the real line satisfying the open set condition (where the open set is an interval). It is well known that the packing dimension of K is equal to α, the unique positive solution y of the equation $ \sum _{j = 1} ^m \rho ^y _{j = 1} $; and the α–dimensional packing measure 𝒫α(K) is finite and positive. Denote by μ the unique self–similar measure for the IFS $ \{ S _j \} ^m _{j=1} $ with the probability weight $ \{ \rho ^\alpha _j \} ^m _{j=1} $. In this paper, we prove that 𝒫α(K) is equal to the reciprocal of the so–called “minimal centered density” of μ, and this yields an explicit formula of 𝒫α(K) in terms of the parameters ρj, bj (j = 1, …, m). Our result implies that 𝒫α(K) depends continuously on the parameters whenever $ \sum _j \rho_j < 1 $.
