Weakly Mixing Systems with Dense Prime Orbits

TL;DR

This paper demonstrates the existence of smooth, weakly mixing reparametrizations of certain linear flows on the torus where all prime-time sampled orbits are dense, revealing new dynamical behaviors.

Contribution

It introduces new examples of weakly mixing systems with dense prime orbits, expanding understanding of orbit density in dynamical systems.

Findings

Existence of smooth, weakly mixing reparametrizations on $ op^2$

All prime-time sampled orbits are dense in these systems

Advances understanding of orbit distribution in weakly mixing flows

Abstract

We show existence of smooth, weakly mixing reparametrizations of some linear flows on $\mathbb{T}^2$ for which all orbits sampled at prime times are dense.