The ω-limit sets of alternating systems

Abstract

Let f and g be elements of with . We study ω-limit sets generated by alternating trajectories of the form . In particular, we prove the following:

1.	A non-empty subset E of I is an ω-limit set for a continuous alternating system defined on I if and only if E is either a closed nowhere dense set or a union of finitely many disjoint non-degenerate closed intervals.
2.	The space of ω-limit sets is closed with respect to the Hausdorff metric.

Keywords:

• continuous alternating system
• topological semiconjugation
• ω-limit set

2000 Mathematics Subject Classification::

• Primary: 37E05
• Secondary: 37E99

Acknowledgements

This research has been partially supported by Ministero dell'Università e della Ricerca Scientifica e Tecnologica, Italy (PRIN 2007: `Valore ed equità in mercati con progetti pubblici ed informazione asimmetrica').

Notes

1. Email: [email protected]

Additional information

Notes on contributors

T. H. Steele

1