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arXiv · 1701.08440

Renewal theorems and mixing for non Markov flows with infinite measure

Ian Melbourne·Dalia Terhesiu
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Abstract

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.

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Ian Melbourne, Dalia Terhesiu. 2019-02-13. Renewal theorems and mixing for non Markov flows with infinite measure. https://arxiv.org/abs/1701.08440

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