International Journal of Mathematics and Mathematical Sciences
Volume 2006 (2006), Article ID 82623, 15 pages
Continuity of the maps and
Department of Mathematics, Weber State University, Ogden 84408-1702, UT, USA
Received 29 September 2004; Revised 11 December 2005; Accepted 12 February 2006
Copyright © 2006 T. H. Steele. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
We study the behavior of two maps in an effort to better
understand the stability of -limit sets as we perturb either or , or both. The first map is the
set-valued function taking in to its collection of -limit points , and the second is the map taking in to its collection of -limit sets . We characterize those functions
in at which each of our maps and is continuous, and then go on to show that both and are continuous on a residual subset of . We then
investigate the relationship between the continuity of and at some function in with the chaotic
nature of that function.