论文标题
与完整连接的随机系统中的度量几何形状
Geometry of measures in random systems with complete connections
论文作者
论文摘要
我们研究具有重叠，薄弱的内态性和具有完整连接的随机系统之间的可数迭代功能系统（IFS）之间的新关系。我们证明，具有重叠和依赖性概率的可计数总条件的固定度量是确切的。此外，我们确定了他们的Hausdorff维度。接下来，我们在具有重叠s的可数IF的极限集中构建了一个分形家族，并研究了这些亚物质支持的某些度量的维度。特别是，我们获得了与系统几何形状有关的这些亚侵点的措施家族。
We study new relations between countable iterated function systems (IFS) with overlaps, Smale endomorphisms and random systems with complete connections. We prove that stationary measures for countable conformal IFS with overlaps and placedependent probabilities, are exact dimensional; moreover we determine their Hausdorff dimension. Next, we construct a family of fractals in the limit set of a countable IFS with overlaps S, and study the dimension for certain measures supported on these subfractals. In particular, we obtain families of measures on these subfractals which are related to the geometry of the system.
