Universal topological models exist for automorphisms with relative discrete spectrum and related classes, enabling orthogonality transfer, while zero-entropy systems with countable eigenvalues satisfy Sarnak's conjecture along a full logarithmic density subsequence.
de la Rue,Notes on Austin’s multiple ergodic theorem, http://hal.archives-ouvertes.fr/hal-00400975
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Unveiling universality, encloseness, and orthogonality in dynamics
Universal topological models exist for automorphisms with relative discrete spectrum and related classes, enabling orthogonality transfer, while zero-entropy systems with countable eigenvalues satisfy Sarnak's conjecture along a full logarithmic density subsequence.