Real-analytic diffeomorphisms with homogeneous spectrum and disjointness of convolutions

Abstract

On any torus ${\mathbb{T}}^d$, $d\ge 2$, 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.

29 pages, 2 figures. arXiv admin note: text overlap with arXiv:1611.06621

References in corpus (1)

• Homogeneous spectrum, Disjointness of Convolutions, and Mixing Properties of Dynamical Systems