Quasi-disjointness and strong quasi-disjointness are defined for minimal systems with equivalent characterizations and preservation under factors, proximal extensions and group extensions, yielding that every minimal PI system is quasi-disjoint from all minimal systems and every AI system is strongl
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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.
A measure-preserving system is U-mixing if and only if it is disjoint from every U-generated system, and every partially rigid system is a finite extension of some U-generated system.
citing papers explorer
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Quasi-disjointness in topological dynamics
Quasi-disjointness and strong quasi-disjointness are defined for minimal systems with equivalent characterizations and preservation under factors, proximal extensions and group extensions, yielding that every minimal PI system is quasi-disjoint from all minimal systems and every AI system is strongl
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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.
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Multipliers and Disjointness from Mixing
A measure-preserving system is U-mixing if and only if it is disjoint from every U-generated system, and every partially rigid system is a finite extension of some U-generated system.