a nontrivial Choquet simplex $K_P$ such that its extreme points $\operatorname{ext}(K_P)$ are dense in $K_P$. By [@LOS] any two nontrivial metrizable Choquet simplices with dense sets of extreme points are equivalent under an affine homeomorphism. Therefore one can speak about *the Poulsen simplex* $K_P$. It is also known that $\operatorname{ext}(K_P)$ is arcwise connected.

Topological dynamics
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We say that $T$ is *transitive* if for every non-empty open sets $U,V\subset X$ there is $n>0$ such that $U\cap T^{-n}(V)\neq\emptyset$. A dynamical system $(X,T)$ is *(topologically) weakly mixing* when the product system $(X\times X,T\times T)$ is topologically transitive. A map $T$ is *(topologically) mixing* if for every non-empty open sets $U,V\subset X$ there is $N\in{\mathbb{N}}$ such that for all $n\ge N$ we have $U\cap T^{-n}(V)\neq\emptyset$. We say that a set $K\subset X$ is *$T$-invariant* if $T(K)\subset K$. A *subsystem* of $(X,T)$ is a pair $(K,T)$, where $K\subset X$ is a nonempty closed $T$-invariant set. Here and elsewhere, we make no distinction between $T$ and its restriction $T|_K$ to a $T$-invariant set $K$ and we often identify a subsystem $(K,T)$ with the set $K$ alone. We say that nonempty closed and $T$-invariant set $K\subset X$ is a *minimal set* for $(X,T)$ if $(K,T)$ does 