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Symbolic dynamics and omega-limit sets of piecewise monotone maps
by
Andy Barwell
University of Birmingham, UK
An omega-limit set L is a closed, invariant, non-empty set which is known to have the property of internal chain transitivity, which says that for any pair of points x and y in L and real number r>0 there is an r-pseudo-orbit in L between x and y. We call a piecewise monotone map locally pre-critical if for any open interval U there is a positive integer k for which fk(U) contains a critical point.
In this talk we demonstrate that for a locally pre-critical piecewise monotone map of the interval, internal chain transitivity characterizes those omega-limit sets which do not contain the image of any critical point. We also demonstrate how symbolic dynamics can be used to identify all points in any omega-limit set of such a map.
Date received: February 20, 2009
Copyright © 2009 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 # cayo-19.