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Invariant subsets of z -> z^2$z \mapsto z^2$

Where can I find an explicit construction of closed invariant subsets of the map z \to z^2$z \mapsto z^2$ on the unit circle? Furstenberg mentions that there are continuum of such disjoint minimal sets but does not provide specific details.

Invariant subsets of z -> z^2

Where can I find an explicit construction of closed invariant subsets of the map z \to z^2 on the unit circle? Furstenberg mentions that there are continuum of such disjoint minimal sets but does not provide specific details.

Invariant subsets of $z \mapsto z^2$

Where can I find an explicit construction of closed invariant subsets of the map $z \mapsto z^2$ on the unit circle? Furstenberg mentions that there are continuum of such disjoint minimal sets but does not provide specific details.

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Invariant subsets of z -> z^2

Where can I find an explicit construction of closed invariant subsets of the map z \to z^2 on the unit circle? Furstenberg mentions that there are continuum of such disjoint minimal sets but does not provide specific details.