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SumTopo 2001, Sixteenth Summer Conference on Topology and its Applications
July 18-21, 2001
City College of CUNY
New York, NY, USA

Organizers
Ralph Kopperman (City College, CUNY), Susan Andima (CW Post College, LIU), Gerald Itzkowitz (Queens College, CUNY), Prabudh Misra (College of Staten Island, CUNY), Shelly Rothman (CW Post College, LIU), Aaron Todd (Baruch College, CUNY)

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The Dynamics of Rational Maps of 2 x 2 Real Matrices
by
Amanda Katharine Schermer
Boston University

We investigate the dynamics induced by rational maps of the form
RC(Z)=an Zn + ... + a1 Z + a-1 Z-1 + ... + a-m Z-m + C
where the ai are real numbers, and the variable Z and constant C are real 2×2 matrices. It is well known that for rational maps of the complex plane of degree at least 2, every attracting cycle must attract the orbit of a critical point. However, in the case of rational matrix maps it is possible for attracting cycles to exist which do not attract a critical orbit. We present evidence that suggests that the existence of these renegade attracting cycles may nevertheless depend on the existence of attracting cycles which do attract critical orbits.

Date received: May 14, 2001

Copyright © 2001 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cagw-37.