F. Abdedou, B. R. Fayad, J.-P. Thouvenot, “Inducing countable Lebesgue spectrum”, Teor. Veroyatnost. i Primenen., 2025, Volume 70, Issue 4,Pages <nobr>764

Inducing countable Lebesgue spectrum

F. Abdedou^a, B. R. Fayad^b, J.-P. Thouvenot^c

^a Institut de Mathématiques de Jussieu-Paris Rive Gauche, Paris, France
^b Department of Mathematics, University of Maryland, USA
^c Laboratoire de Probabilités, Statistique et Modélisation, Sorbonne Université, Paris, France

Abstract: We show that any ergodic dynamical system generates a system with pure Lebesgue spectrum of infinite multiplicity.

Keywords: dynamical system, spectral theory of dynamical systems, Koopman operator, ergodic theory, induced transformation (first return map), infinite spectral multiplicity.

Received: 16.08.2025
Revised: 07.09.2025
Accepted: 16.08.2025

Language: English

DOI: 10.4213/tvp5874