TY - JOUR
T1 - Attractors of directed graph IFSs that are not standard IFS attractors and their Hausdorff measure
AU - Boore, Graeme
AU - Falconer, Kenneth John
N1 - "GCB was supported by an EPSRC Doctoral Training Grant whilst undertaking this work"
PY - 2013
Y1 - 2013
N2 - For directed graph iterated function systems (IFSs) defined on R, we prove that a class of 2-vertex directed graph IFSs have attractors that cannot be the attractors of standard (1-vertex directed graph) IFSs, with or without separation conditions. We also calculate their exact Hausdorff measure. Thus we are able to identify a new class of attractors for which the exact Hausdorff measure is known.
AB - For directed graph iterated function systems (IFSs) defined on R, we prove that a class of 2-vertex directed graph IFSs have attractors that cannot be the attractors of standard (1-vertex directed graph) IFSs, with or without separation conditions. We also calculate their exact Hausdorff measure. Thus we are able to identify a new class of attractors for which the exact Hausdorff measure is known.
UR - http://journals.cambridge.org/abstract_S0305004112000576
U2 - 10.1017/S0305004112000576
DO - 10.1017/S0305004112000576
M3 - Article
SN - 0305-0041
VL - 154
SP - 325
EP - 349
JO - Mathematical Proceedings of the Cambridge Philosophical Society
JF - Mathematical Proceedings of the Cambridge Philosophical Society
IS - 02
ER -