M\"obius Disjointness for Skew Products on the Heisenberg Nilmanifold

TL;DR

This paper proves that the Möbius function exhibits disjointness from a class of skew product dynamical systems on the Heisenberg nilmanifold, extending understanding of Möbius disjointness in complex dynamical settings.

Contribution

It establishes Möbius disjointness for Lipschitz skew products on the Heisenberg nilmanifold, a significant advancement in understanding Möbius disjointness in non-abelian nilmanifolds.

Findings

Möbius function is disjoint from Lipschitz skew products on the Heisenberg nilmanifold

Disjointness holds over minimal rotations of the 2D torus

Extends Möbius disjointness results to non-abelian nilmanifolds

Abstract

We prove that the M\"obius function is disjoint to all Lipschitz continuous skew product dynamical systems on the 3-dimensional Heisenberg nilmanifold over a minimal rotation of the 2-dimensional torus.