Real-analytic diffeomorphisms with homogeneous spectrum and disjointness of convolutions

TL;DR

This paper constructs a real-analytic diffeomorphism on higher-dimensional tori with specific spectral properties, including disjointness of convolutions and homogeneous spectrum of multiplicity two, using an advanced approximation method.

Contribution

It introduces a real-analytic version of the Approximation by Conjugation-method to produce diffeomorphisms with novel spectral characteristics on tori.

Findings

Existence of diffeomorphisms with disjoint convolution spectra

Construction of diffeomorphisms with homogeneous spectrum of multiplicity two

Application of real-analytic approximation techniques

Abstract

On any torus $\mathbb{T}^d$, $d \geq 2$, we prove the existence of a real-analytic diffeomorphism $T$ with a good approximation of type $\left(h,h+1\right)$, a maximal spectral type disjoint with its convolutions and a homogeneous spectrum of multiplicity two for the Cartesian square $T\times T$. The proof is based on a real-analytic version of the Approximation by Conjugation-method.