On Schmidt's game and the set of points with non-dense orbits under a class of expanding maps
On Schmidt's game and the set of points with non-dense orbits under a class of expanding maps
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DOI：
10.1016/j.jmaa.2014.04.026
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发表时间：
2014-10
影响因子：
1.3
通讯作者：
Hui Hu;Yue-Li Yu
中科院分区：
文献类型：
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作者：
Hui Hu;Yue-Li Yu
在给定一个扩张区间映射的情况下，我们考虑向前轨道远离给定点的点集。对于一类扩展区间映射，包括高斯变换和所有的Beta变换，证明了这类集合在Schmidt博弈意义下是1/2获胜的。这是在W·施密特工作成果的基础上改进的。
Given an expanding interval map, we consider sets of points whose forward orbits are bounded away from a given point. It is shown that such sets are 1/2-winning in the sense of Schmidt's game for a class of expanding interval maps including the Gauss transformation and all beta transformations. This improves upon several results dating back to a work of W. Schmidt.