Gaussian factors, spectra, and $P$-entropy

TL;DR

This paper explores the spectral properties of Gaussian automorphisms, focusing on their entropy and disjointness, revealing new insights into their spectral isomorphism and Lebesgue spectrum characteristics.

Contribution

It introduces a novel analysis of Gaussian automorphisms with disjoint spectra and their entropy, expanding understanding of spectral isomorphism in ergodic theory.

Findings

Existence of disjoint Gaussian automorphisms with Lebesgue spectrum

Spectral isomorphism of even factors in Gaussian automorphisms

New relationships between spectra and P-entropy in Gaussian systems

Abstract

There is a set of continual cardinality of pairwise disjoint Gaussian automorphisms with spectrally isomorphic even factors having Lebesgue spectrum.