论文标题
自相似于重叠结构的量化维度
Quantization dimension for self-similar measures of overlapping construction
论文作者
论文摘要
已经计算了针对具有良好分离圆柱体的动态定义分形的许多不变测量的量化维度，也就是说，在所谓的开放式环境（OSC）保持的情况下。在圆柱体之间存在重叠的情况下，我们考虑了一个自相似措施的家族，为此，基础迭代功能系统满足所谓的弱分离特性（WSP），但由于完全重叠的速度发生在圆柱体之间。本文中的工作还表明，满足WSP的重叠自相似结构确定的量化维度与热力学形式主义的温度函数有关系。
Quantization dimension has been computed for many invariant measures of dynamically defined fractals having well separated cylinders, that is, in the cases when the so-called Open Set Condition (OSC) holds. To attack the same problem in case of heavy overlaps between the cylinders, we consider a family of self-similar measures, for which the underlying Iterated Function System satisfies the so-called Weak Separation Property (WSP) but does not satisfy the OSC since complete overlaps occur in between the cylinders. The work in this paper also shows that the quantization dimension determined for the set of overlap self-similar construction satisfying the WSP has a relationship with the temperature function of the thermodynamic formalism.
