Affiliation:
1. Department of Mathematics, University of Delhi, Delhi, India
Abstract
In this paper, the notions of topological shadowing, topological ergodic
shadowing, topological chain transitivity and topological chain mixing are
introduced and studied for an iterated function system (IFS) on uniform
spaces. It is proved that if an IFS has topological shadowing property and
is topological chain mixing, then it has topological ergodic shadowing and
it is topological mixing. Moreover, if an IFS has topological shadowing
property and is topological chain transitive, then it is topologically
ergodic and hence topologically transitive. Also, these notions are studied
for the product IFS on uniform spaces.
Publisher
National Library of Serbia