An open set of maps for which every point is absolutely nonshadowable
by
Guocheng Yuan
University of Maryland at College Park
Coauthors: James A. Yorke

We say an attractor has the property of dimension variablity if there are periodic points in this attractor whose unstable dimensions are different. Under the condition that there exists a direction which is more expanding than other directions, we prove that such attractors are nonshadowable. Using this theorem, we prove that there is an open set of diffeomorphisms (in the C^r-topology, r > 1) for which every point is absolutely nonshadowable, i. e. , there exists \epsilon > 0 such that for every \delta > 0, almost every \delta-pseudo trajectory starting from this point is \epsilon-nonshadowable.

Date received: March 17, 1998

Copyright © 1998 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 Mathematical Conference Abstracts. Document # cabf-21.