论文标题
与三个地图的同质系统相关的自相似措施
Self-similar measures associated to a homogeneous system of three maps
论文作者
论文摘要
我们研究了与$ \ bf r $和其他更一般IFS的三个合同相似性的均质迭代功能系统相关的自相似措施的维度。我们将最近为Bernoulli卷积开发的一些理论扩展到了这种环境。在三张地图的设置中，发生了新现象，这是贝克最近的例子和贝拉尼（Käenmäki）的近期例子所强调的。为了克服这些困难，我们开发了新的技术，包括将霍克曼熵增加方法扩展到功能场设置。
We study the dimension of self-similar measures associated to a homogeneous iterated function system of three contracting similarities on $\bf R$ and other more general IFS's. We extend some of the theory recently developed for Bernoulli convolutions to this setting. In the setting of three maps a new phenomenon occurs, which has been highlighted by recent examples of Baker, and Bárány, Käenmäki. To overcome the difficulties stemming form these, we develop novel techniques, including an extension of Hochman's entropy increase method to a function field setup.
