Analytic reparametrizations of translation toral flows with countable Lebesgue spectrum

TL;DR

This paper presents an example of a real analytic reparametrization of a minimal translation flow on a 5-dimensional torus that exhibits a Lebesgue spectrum with infinite multiplicity, advancing understanding of spectral properties of dynamical systems.

Contribution

It introduces a specific real analytic reparametrization of a translation flow with Lebesgue spectrum of infinite multiplicity, a novel example in the study of spectral types.

Findings

Existence of a real analytic reparametrization with Lebesgue spectrum

The reparametrized flow has infinite spectral multiplicity

Advances understanding of spectral properties in translation flows

Abstract

We give an example of a real analytic reparametrization of a minimal translation flow on $\mathbb{T}^{5}$ that has a Lebesgue spectrum with infinite multiplicity.