Uncountable ω-limit sets with isolated points

Christopher Good, BE Raines, R Suabedissen

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)


We give two examples of tent maps with uncountable (as it happens, post-critical) omega-limit sets, which have isolated points, with interesting structures. Such omega-limit sets must be of the form C boolean OR 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 omega-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 omega-limit set is uncountable. Secondly, we give an example of an omega-limit set of the form C boolean OR R for which the Cantor set C is minimal.
Original languageEnglish
Pages (from-to)179-189
Number of pages11
JournalFundamenta Mathematicae
Issue number2
Publication statusPublished - 1 Jan 2009


  • limit type
  • interval map
  • omega limit set
  • unimodal
  • attractor
  • invariant set


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