Polynomial rigidity and spectrum of Sidon automorphisms

2023/10/16 by Ryzhikov, Valery V. · 1 citation
#Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.2310.10370

Abstract

We present spectrally disjoint Sidon automorphisms whose tensor squares are isomorphic to a planar shift. Spectra of such automorphisms do not possess the group property. To check the singularity of spectrum, we use polynomial rigidity of operators associated with Kolmogorov linear determinism. In the class of mixing Gaussian and Poisson suspensions we realize new sets of spectral multiplicities.

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• Continuum pairwise disjoint automorphisms with Lebesgue spectrum

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