TY - JOUR
T1 - The conley attractors of an iterated function system
AU - Barnsley, Michael F.
AU - Vince, Andrew
PY - 2013/10
Y1 - 2013/10
N2 - Abstract We investigate the topological and metric properties of attractors of an iterated function system (IFS) whose functions may not be contractive. We focus, in particular, on invertible IFSs of finitely many maps on a compact metric space. We rely on ideas of Kieninger [Iterated Function Systems on Compact Hausdorff Spaces (Shaker, Aachen, 2002)] and McGehee and Wiandt ['Conley decomposition for closed relations', Differ. Equ. Appl. 12 (2006), 1-47] restricted to what is, in many ways, a simpler setting, but focused on a special type of attractor, namely point-fibred invariant sets. This allows us to give short proofs of some of the key ideas.
AB - Abstract We investigate the topological and metric properties of attractors of an iterated function system (IFS) whose functions may not be contractive. We focus, in particular, on invertible IFSs of finitely many maps on a compact metric space. We rely on ideas of Kieninger [Iterated Function Systems on Compact Hausdorff Spaces (Shaker, Aachen, 2002)] and McGehee and Wiandt ['Conley decomposition for closed relations', Differ. Equ. Appl. 12 (2006), 1-47] restricted to what is, in many ways, a simpler setting, but focused on a special type of attractor, namely point-fibred invariant sets. This allows us to give short proofs of some of the key ideas.
KW - Keywords and phrases iterated function system
KW - attractor-repeller
UR - http://www.scopus.com/inward/record.url?scp=84883641718&partnerID=8YFLogxK
U2 - 10.1017/S0004972713000348
DO - 10.1017/S0004972713000348
M3 - Article
SN - 0004-9727
VL - 88
SP - 267
EP - 279
JO - Bulletin of the Australian Mathematical Society
JF - Bulletin of the Australian Mathematical Society
IS - 2
ER -