Continuum pairwise disjoint automorphisms with Lebesgue spectrum

TL;DR

This paper constructs a continuous family of Gaussian suspension factors for Sidon transformations that are pairwise disjoint, share the same Lebesgue spectrum, but differ in their entropy, advancing understanding of spectral properties in ergodic theory.

Contribution

It introduces a novel family of disjoint Gaussian suspension factors with identical Lebesgue spectrum but varying entropy, expanding the class of known spectral phenomena in ergodic systems.

Findings

Family of pairwise disjoint factors constructed

All factors have Lebesgue spectrum

Factors exhibit different entropy values

Abstract

A continuous family of pairwise disjoint even factors of Gaussian suspensions for Sidon transformations is presented. These factors have the same Lebesgue spectrum, but different Kirillov-Kushnirenko entropy.