An \(\omega \)-limit set for a Lipschitz function with zero topological entropy (Q1978866)

If \(Q\) is the classical Cantor set on \([0,1]\) and \(C\) is the countable set of midpoints of the intervals complementary to \(Q\) together with the one-point set \(\{-\frac {1}{6}\}\) then a zero topological entropy Lipschitz function \(f\) mapping \([-\frac {1}{4},1]\) into itself is constructed in such a way that the set \(Q\cup C\) is its \(\omega \)-limit set.