TY - JOUR
T1 - Real projective iterated function systems
AU - Barnsley, Michael F.
AU - Vince, Andrew
PY - 2012/10
Y1 - 2012/10
N2 - This paper contains four main results associated with an attractor of a projective iterated function system (IFS). The first theorem characterizes when a projective IFS has an attractor which avoids a hyperplane. The second theorem establishes that a projective IFS has at most one attractor. In the third theorem the classical duality between points and hyperplanes in projective space leads to connections between attractors that avoid hyperplanes and repellers that avoid points, as well as hyperplane attractors that avoid points and repellers that avoid hyperplanes. Finally, an index is defined for attractors which avoid a hyperplane. This index is shown to be a nontrivial projective invariant.
AB - This paper contains four main results associated with an attractor of a projective iterated function system (IFS). The first theorem characterizes when a projective IFS has an attractor which avoids a hyperplane. The second theorem establishes that a projective IFS has at most one attractor. In the third theorem the classical duality between points and hyperplanes in projective space leads to connections between attractors that avoid hyperplanes and repellers that avoid points, as well as hyperplane attractors that avoid points and repellers that avoid hyperplanes. Finally, an index is defined for attractors which avoid a hyperplane. This index is shown to be a nontrivial projective invariant.
KW - Attractor
KW - Iterated function system
KW - Projective space
UR - http://www.scopus.com/inward/record.url?scp=84869490174&partnerID=8YFLogxK
U2 - 10.1007/s12220-011-9232-x
DO - 10.1007/s12220-011-9232-x
M3 - Article
SN - 1050-6926
VL - 22
SP - 1137
EP - 1172
JO - Journal of Geometric Analysis
JF - Journal of Geometric Analysis
IS - 4
ER -