Journal of Prime Research in Mathematics
Vol. 1 (2008), Issue 1, pp. 101 – 112
ISSN: 1817-3462 (Online) 1818-5495 (Print)
ISSN: 1817-3462 (Online) 1818-5495 (Print)
Limit sets of weakly contracting relations with eventual condensation
Vasile Glavan
Moldova State University, 60 A.Mateevici St., Chisinau, Republic of Moldova; University of Podlasie, Ul. Konarskiego 2, Siedlce, Poland.
Valeriu Gutu
Moldova State University, 60 A.Mateevici St., Chisinau, Republic of Moldova.
\(^{1}\)Corresponding Author: vglavan@ap.siedlce.pl
Copyright © 2008 Vasile Glavan, Valeriu Gutu. 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.
Published: December, 2005
Abstract
Barnsley’s formula for the attractor of a hyperbolic IFS with condensation is generalized for the omega-limit set of a weakly contracting set-valued map with eventual condensation. The latter need not be a contraction, as well as its omega-limit set need not be an attractor.
Keywords:
Set-valued map, weak contraction, eventual condensation, attractor, limit relation, limit set, fractal.