# Example of minimal connected weakly mixing dynamical system

I am looking for an example of a dynamical system $$(X,T)$$ such that:

• $$X$$ is a connected topological space,
• $$(X,T)$$ is minimal and weakly mixing.

Does there exists one?

To get a diffeomorphism with those properties from such a flow, one can show that given any minimal flow, there is a generic set $$\mathcal{R}\subset\mathbb{R}$$ such that the time-$$t$$ map is indeed minimal for every $$t\in\mathcal{R}$$, and such map must be mixing.