Explicit Infinite Mixing Automorphisms with Simple Spectra of Symmetric Squares

TL;DR

This paper constructs explicit mixing ergodic automorphisms with simple spectra in their symmetric squares, advancing the understanding of spectral properties in dynamical systems.

Contribution

It introduces explicit examples of mixing automorphisms with simple spectra in their symmetric tensor squares, using near-Sidon constructions.

Findings

Constructed mixing automorphisms with simple spectra in symmetric squares

Connected spectral properties to classical dynamical problems

Provided explicit examples in the class of near-Sidon constructions

Abstract

We present mixing ergodic automorphisms of a space with sigma-finite measure whose symmetric tensor squares have simple spectra. This property is of interest in connection with dynamical spectral problems of A.N. Kolmogorov and V.A. Rokhlin. Explicit examples are given in the class of near-Sidon constructions.