Structure and Spectrum of Nonergodic Nilsystems
Dynamical Systems
2026-03-31 v2
Abstract
We study Host-Kra factors and the spectral type of nilsystems, without assuming ergodicity. In the ergodic case, it is known that the spectral type splits into a discrete component and a Lebesgue component of infinite multiplicity. Our main result extends this decomposition to nonergodic nilsystems.
Cite
@article{arxiv.2602.21021,
title = {Structure and Spectrum of Nonergodic Nilsystems},
author = {Felipe Hernández},
journal= {arXiv preprint arXiv:2602.21021},
year = {2026}
}
Comments
We decided to remove Corollary C as there is an overlooked case that does not seem to follow from our main results