Minimal maps need not have Misiurewicz Stroboscopical Property
by
Víctor Jiménez López
Universidad de Murcia (Spain)
Coauthors: L'ubomir Snoha (Matej Bel University, Banská Bystrica, Slovakia)

A continuous map from a metric space into itself is said to have Misiurewicz stroboscopical property if, given any point z from the space and any increasing sequence of positive integers, there is a point whose omega-limit set relative to this sequence contains z.

We show that there is a minimal triangular homeomorphism on the torus which does not have such property. This gives a negative answer to a question posed by M. Misiurewicz whether minimal maps in compact metric spaces always have this property.

We also show that equicontinuous minimal systems in compact metric spaces and topologically strongly mixing (not necessarily minimal) systems in locally compact metric spaces do have Misiurewicz stroboscopical property.

Date received: February 26, 2001

Copyright © 2001 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cafw-32.