论文标题
没有$σ$ -Finite绝对连续的多政治圆形图
There are no $σ$-finite absolutely continuous invariant measures for multicritical circle maps
论文作者
论文摘要
众所周知，每个没有周期性轨道的多政治圆形图都承认了一个独特的不变的borel概率措施，该概率措施纯粹相对于Lebesgue度量而言是单数的。这样的地图能否留下不变的无限，$σ$ - 最终不变的度量，与Lebesgue度量绝对是连续的？在本文中，使用Katznelson引起的旧标准，我们证明了这个问题的答案是否定的。
It is well-known that every multicritical circle map without periodic orbits admits a unique invariant Borel probability measure which is purely singular with respect to Lebesgue measure. Can such a map leave invariant an infinite, $σ$-finite invariant measure which is absolutely continuous with respect to Lebesgue measure? In this paper, using an old criterion due to Katznelson, we show that the answer to this question is no.
