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Journal of Geometric Analysis

, Volume 22, Issue 4, pp 1137–1172 | Cite as

Real Projective Iterated Function Systems

  • Michael F. Barnsley
  • Andrew Vince
Article

Abstract

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.

Keywords

Iterated function system Attractor Projective space 

Mathematics Subject Classification (2000)

28A80 

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Copyright information

© Mathematica Josephina, Inc. 2011

Authors and Affiliations

  1. 1.Department of MathematicsAustralian National UniversityCanberraAustralia
  2. 2.Department of MathematicsUniversity of FloridaGainesvilleUSA

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