论文标题
依赖路径的缩小靶标在通用仿期迭代功能系统中
Path-dependent shrinking targets in generic affine iterated function systems
论文作者
论文摘要
我们计算通用仿射迭代功能系统中路径依赖性缩小目标集的Hausdorff维度。在这里，通过依赖路径的缩小目标集，我们的意思是一组点，其轨道通常无限地击中带有固定通用中心的小球，半径降低并取决于点本身。事实证明，这种集合的Hausdorff尺寸由特定LIMSUP压力函数的零点给出。结果概括了Koivusalo和Ramirez，Barany和Troscheit以及Hill和Velani的工作。
We calculate the Hausdorff dimension of path-dependent shrinking target sets in generic affine iterated function systems. Here, by a path-dependent shrinking target set, we mean a set of points whose orbits infinitely often hit small balls with a fixed generic centre and with radius decreasing and dependent on the point itself. It turns out that the Hausdorff dimension of such a set is given by the zero point of a certain limsup pressure function. The result generalizes the work of Koivusalo and Ramirez, and Barany and Troscheit, as well as that of Hill and Velani.
