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 -