# Mixing for Smooth Time-Changes of General Nilflows

## TL;DR

This paper demonstrates that for a broad class of nilflows, generic smooth time-changes induce mixing behavior, extending previous results from specific cases to more general nilmanifolds of step at least 2.

## Contribution

It proves that a dense set of smooth time-changes on any nilmanifold of step at least 2 lead to mixing nilflows, generalizing earlier results from Heisenberg to arbitrary nilflows.

## Key findings

- Existence of a dense set of smooth time-changes inducing mixing.
- Generalization of mixing results from Heisenberg to all nilflows of step ≥ 2.
- Mixing behavior occurs for non-trivially time-changed nilflows.

## Abstract

We consider completely irrational nilflows on any nilmanifold of step at least $2$. We show that there exists a dense set of smooth time-changes such that any time-change in this class which is not measurably trivial gives rise to a mixing nilflow. This in particular reproves and generalizes to any nilflow (of step at least $2$) the main result proved in [AFU] for the special class of Heisenberg (step $2$) nilflows, and later generalized in [Rav2] to a class of nilflows of arbitrary step which are isomorphic to suspensions of higher-dimensional linear toral skew-shifts.