English

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

R2 v1 2026-07-01T10:50:14.562Z