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The following problem is presented in the paper Recent development of chaos theory in topological dynamics - by Jian Li and Xiangdong Ye : "If a dynamical system [$(X,f)$, $X$ metric space, $f$ ...

Let $X$ be a compact metric space, $X*X$ its cartesian product, and $A$ a subset of $X*X$. Are the following two properties the same, or e.g. one is stronger than the other? $A$ is dense and residual ...

This question is cross-posted from MSE, since it hasn't gotten an answer there for over 72 hours. Wikipedia gives essentially "is topologically mixing and has dense periodic periodic orbits"...