The dynamical Borel-Cantelli lemma for interval maps
The dynamical Borel-Cantelli lemma for interval maps
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DOI：
10.3934/dcds.2007.17.891
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发表时间：
2007-04-01
影响因子：
1.1
通讯作者：
Kim, Dong Han
中科院分区：
文献类型：
--
作者：
Kim, Dong Han
研究了一类区间映射的动力学Borel-Cantelli引理。对于导数有界变差的扩张映射，任何区间序列都满足动力学Borel-Cantelli引理。如果一个映射有一个中立不动点，那么即使在映射有有限个绝对连续不变测度和可加衰减相关的情况下，动力学Borel-Cantelli引理也不成立。
The dynamical Borel-Cantelli lemma for some interval maps is considered. For expanding maps whose derivative has bounded variation, any sequence of intervals satisfies the dynamical Borel-Cantelli lemma. If a map has an indifferent fixed point, then the dynamical Borel-Cantelli lemma does not hold even in the case that the map has a finite absolutely continuous invariant measure and summable decay of correlations.