Invariant scrambled sets, uniform rigidity and weak mixing
  We show that for a non-trivial transitive dynamical system, it has a dense Mycielski invariant strongly scrambled set if and only if it has a fixed point, and it has a dense Mycielski invariant $\delta$-scrambled set for some $\delta>0$ if and only if it has a fixed point and not uniformly rigid. We also provide two methods for the construction of completely scrambled systems which are weakly mixing, proximal and uniformly rigid. 
Magdalena Fory\'s, Wen Huang, Jian Li, Piotr Oprocha
math.DS