Local limit theorems for suspended semiflows

TL;DR

This paper establishes local limit theorems and mixing properties for cocycles over semiflows, including hyperbolic geodesic flows, advancing the understanding of statistical behaviors in dynamical systems.

Contribution

It introduces new local limit theorems for cocycles over semiflows and demonstrates mixing properties like rational weak mixing in specific skew product semiflows.

Findings

Proved local limit theorems for cocycles over semiflows.

Established rational weak mixing for certain skew product semiflows.

Analyzed mixing properties of hyperbolic geodesic flows of cyclic covers.

Abstract

We prove local limit theorems for a cocycle over a semiflow by establishing topological, mixing properties of the associated skew product semiflow. We also establish conditional rational weak mixing of certain skew product semiflows and various mixing properties including order 2 rational weak mixing of hyperbolic geodesic flows of cyclic covers.