Dynamical systems disjoint from any minimal system

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Recurrence properties and disjointness on the induced spaces (2013, background): “Tk ×Sk-invariant and (µ×ν)(Uc)≤ (µ×ν)((U1 ×U2)c)≤ µ(Uc 1)+ν(U2c)<ε. That is, (X ×Y,T ×S)has almost dense periodic sets. It is well known that a totally transitive P-system is weakly mixing [1]. In [12], Huang and Ye showed that a totally transitive system with dense small periodic sets is weakly ”
Tame systems and scrambled pairs under an Abelian group action (2006, background): “In [19], the author gives an example to show that for a cascade, extreme scattering is strictly weaker than weak mixing.”
Recent development of chaos theory in topological dynamics (2015, background): “We say that a dynamical system (X,T ) has dense small periodic sets [48] if for any non-empty open subset U of X there exists a non-empty closed subset Y of U and k ∈ N such that T Y ⊂ Y .”