Uncountable ω-limit sets with isolated points
We give two examples of tent maps with uncountable (as it happens, post-critical) ω-limit sets, which have isolated points, with interesting structures. Such ω-limit sets must be of the form C ∪ R, where C is a Cantor set and R is a scattered set. Firstly, it is known that there is a restriction on the topological structure of countable ω-limit sets for finite-to-one maps satisfying at least some weak form of expansivity. We show that this restriction does not hold if the ω-limit set is uncountable....