Uncountable ω-limit sets with isolated points

• Autorzy: Chris Good , Brian E. Raines , Rolf Suabedissen
• Języki publikacji: EN

Abstrakty

EN

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. Secondly, we give an example of an ω-limit set of the form C ∪ R for which the Cantor set C is minimal.

Kategorie tematyczne

• 54H20: Topological dynamics
• 54F15: Continua and generalizations
• 37B45: Continua theory in dynamics
• 37E05: Maps of the interval (piecewise continuous, continuous, smooth)

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2009
• Tom: 205
• Numer: 2
• Strony: 179-189

Daty

wydano

2009

Twórcy

autor

Chris Good

• School of Mathematics and Statistics, University of Birmingham, Birmingham, B15 2TT, UK

autor

Brian E. Raines

• Department of Mathematics, Baylor University, Waco, TX 76798-7328, U.S.A.

autor

Rolf Suabedissen

• Mathematical Institute, University of Oxford, Oxford, OX1 3LB, UK

Identyfikatory

DOI

10.4064/fm205-2-6