Renewal theorems and mixing for non Markov flows with infinite measure
Renewal theorems and mixing for non Markov flows with infinite measure
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DOI：
10.1214/19-aihp968
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发表时间：
2020-02-01
影响因子：
1.5
通讯作者：
Terhesiu, Dalia
中科院分区：
文献类型：
--
作者：
Melbourne, Ian;Terhesiu, Dalia
我们得到的结果混合的一大类（不一定马尔可夫）无限测度半流和流。埃里克森证明，除其他事项外，强更新定理在相应的i.i.d.设置.利用算子更新理论，我们将埃里克森的方法扩展到确定性（即非独立同分布）。我们的结果适用于Pomeau-Manneville型的间歇半流和流（包括Markov和nonMarkov），以及具有不可积屋顶函数的Collet-Eckmann映射上的半流和流。
We obtain results on mixing for a large class of (not necessarily Markov) infinite measure semiflows and flows. Erickson proved, amongst other things, a strong renewal theorem in the corresponding i.i.d. setting. Using operator renewal theory, we extend Erickson's methods to the deterministic (i.e. non-i.i.d.) continuous time setting and obtain results on mixing as a consequence.Our results apply to intermittent semiflows and flows of Pomeau-Manneville type (both Markov and nonMarkov), and to semiflows and flows over Collet-Eckmann maps with nonintegrable roof function.