- CARMA SEMINAR
- Speaker: Prof Michael Barnsley, Mathematical Sciences Institute, Australian National University
- Title: Real Projective Iterated Function Systems
- Location: Room VG10, Mathematics Building (Callaghan Campus) The University of Newcastle
- Time and Date: 10:30 am, Fri, 11th Jun 2010
I will describe four recent theorems, developed jointly with Andrew Vince and David C. Wilson (both of the University of Florida) that reveal a surprisingly rich theory associated with an attractor of a projective iterated function system (IFS). The first theorem characterizes when a projective IFS has an attractor that 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 and an associated index, which is a nontrivial projective invariant, is defined. I will link these results to the Conley decomposition theorem.
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