Real projective iterated function systems

Michael F. Barnsley*, Andrew Vince

*Corresponding author for this work

    Research output: Contribution to journalArticlepeer-review

    26 Citations (Scopus)

    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.

    Original languageEnglish
    Pages (from-to)1137-1172
    Number of pages36
    JournalJournal of Geometric Analysis
    Volume22
    Issue number4
    DOIs
    Publication statusPublished - Oct 2012

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