Projection pressure and Bowen’s equation for a class of self-similar fractals with overlap structure
Projection pressure and Bowen’s equation for a class of self-similar fractals with overlap structure
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DOI：
10.1007/s11425-012-4412-0
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发表时间：
2010-03
期刊：
影响因子：
--
通讯作者：
Chenwei Wang;Ercai Chen
中科院分区：
文献类型：
--
作者：
Chenwei Wang;Ercai Chen
设{Si}i= 1 l是一个具有吸引子K的迭代函数系。设π是正则投影。本文在一定的仿射IFS下，定义了一个新的概念--投影压力Pπ（φ），其中φ∈C（φ d），并给出了投影压力的变分原理.此外，我们还检验了当每个Si是具有相同压缩比的相似映射时，“投影压力”的唯一零根仍然满足Bowen方程。利用Bowen方程的根，我们可以得到吸引子K的Hausdorff维数。
Let {Si}i=1lbe an iterated function system (IFS) on ℝdwith attractor K. Letπbe the canonical projection. In this paper, we define a new concept called “projection pressure”Pπ(φ) forφ∈C(ℝd) under certain affine IFS, and show the variational principle about the projection pressure. Furthermore, we check that the unique zero root of “projection pressure” still satisfies Bowen’s equation when eachSiis the similar map with the same compression ratio. Using the root of Bowen’s equation, we can get the Hausdorff dimension of the attractorK.