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Schmidt’s game and nonuniformly expanding interval maps
Nonlinearity ( IF 1.7 ) Pub Date : 2020-09-30 , DOI: 10.1088/1361-6544/ab972a
Jason Duvall

We study Manneville-Pomeau maps on the unit interval and 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.

中文翻译:

施密特的博弈和非均匀扩展区间图

我们研究了单位间隔上的 Manneville-Pomeau 映射,并证明了前向轨道错过了左端点 0 的间隔的点集对于施密特的游戏来说是强有力的胜利。强赢集是稠密的,具有完整的 Hausdorff 维,并且满足可数交集。对于某些扩展地图,类似的结果是已知的,但这些并没有解决非均匀扩展的情况。由于存在无限失真和无限几何,我们的分析变得复杂。
更新日期:2020-09-30
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