# Renewal theorems and mixing for non Markov flows with infinite measure

## TL;DR

This paper extends renewal theory and mixing results to a broad class of non-Markov, infinite measure semiflows and flows, including intermittent and Collet-Eckmann type systems, using operator renewal techniques.

## Contribution

It develops operator renewal theory for deterministic continuous-time systems, generalizing Erickson's i.i.d. renewal results to non-Markov flows with infinite measure.

## Key findings

- Established mixing results for non-Markov infinite measure semiflows.
- Extended renewal theorems to deterministic continuous-time systems.
- Applied results to intermittent and Collet-Eckmann type flows.

## 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.