Schmidt’s game and nonuniformly expanding interval maps
Schmidt’s game and nonuniformly expanding interval maps
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施密特博弈和非均匀扩展区间图
DOI：
10.1088/1361-6544/ab972a
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发表时间：
2019
期刊：
影响因子：
1.7
通讯作者：
Jason Duvall
中科院分区：
文献类型：
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作者：
Jason Duvall
我们研究了一类中立型不动点在0的非一致扩张区间映射，这类映射包括Manneville-Pomeau映射。我们证明了前向轨道偏离左端点为0的区间的点集在Schmidt博弈中是强获胜的。强赢集是稠密的，具有全Hausdorff维，并且满足可数交性质。已知的某些扩展地图也有类似的结果，但这些结果并没有解决非均匀扩展的情况。我们的分析由于无限变形和无限几何的存在而变得复杂。
We study a class of nonuniformly expanding interval maps with a neutral fixed point at 0, a class that includes Manneville–Pomeau maps. We prove that the set of points whose forward orbits miss an interval with left endpoint 0 is strong winning for Schmidt’s game. Strong winning sets are dense, have full Hausdorff dimension, and satisfy a countable intersection property. Similar results were known for certain expanding maps, but these did not address the nonuniformly expanding case. Our analysis is complicated by the presence of infinite distortion and unbounded geometry.
影响因子：
0.9
作者：
K. Gelfert;M. Rams
通讯作者：
K. Gelfert;M. Rams