旋转β展开的不变测度与一个Tarski问题
Invariant measure of rotational beta expansion and a problem of Tarski
摘要：
研究了扩张相似模格定义的$\mathbb{R}^m$中分段可扩映射的不变测度。利用Bang关于Tarski的一个问题的结果，证明了当相似比不小于$m+1$时，在基本区上的一些温和的假设下，它有一个等价于$m$维勒贝格测度的绝对连续不变测度.将该方法应用于$m=2$的情形，得到了Akiyama-Caalim：2015中结果的另一种证明，并作了一些改进.
英文摘要：
We study invariant measures of a piecewise expanding map in $\mathbb{R}^m$ defined by an expanding similitude modulo lattice. Using the result of Bang on a problem of Tarski, we show that when the similarity ratio is not less than $m+1$, it has an absolutely continuous invariant measure equivalent to the $m$-dimensional Lebesgue measure, under some mild assumption on the fundamental domain. Applying the method to the case $m=2$, we obtain an alternative proof of the result in Akiyama-Caalim:2015 together with some improvement.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
