Renewal theorems and mixing for non Markov flows with infinite measure
Dynamical Systems
2020-02-06 v3
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.
Keywords
Cite
@article{arxiv.1701.08440,
title = {Renewal theorems and mixing for non Markov flows with infinite measure},
author = {Ian Melbourne and Dalia Terhesiu},
journal= {arXiv preprint arXiv:1701.08440},
year = {2020}
}
Comments
Accepted version. To appear in Ann. Inst. H. Poincar\'e (B) Probab. Statist