My research is in the area of holomorphic
dynamics, particularly on the structure of
polynomial Julia sets. Here is a famous Julia
set, the Douady Rabbit.
I have found a new family of metaFibonacci numbers. They occur as the return times of polynomials. I have study the interaction of Brownian motion in the complex plane and Julia sets by coding the Brownian motion on the tree with dynamics. Articles: Dynamics of Polynomials with Disconnected Julia Sets."Discrete and Continuous Dynamical Systems  Series A, Volume 9, Number 4, July 2003. http://aimsciences.org/journals/displayPapers.jsp?comments=&pubID=30&journID=1&pubString=Volume:%209,%20Number:%204,%20July%202003 (Offprints available upon request). A Family of MetaFibonacci Sequences Defined by VariableOrder Recursions. Journal of Integer Sequences, Volume 9, Issue 1, Article 06.1.8, 2006. http://www.cs.uwaterloo.ca/journals/JIS/VOL9/Emerson/emerson6.pdf Return Times of Polynomials as metaFibonacci Numbers. Conformal Geometry and Dynamics, Volume 12, October 2008. http://www.ams.org/ecgd/20081210/S1088417308001835/ Brownian motion, random walks on trees, and harmonic measure on polynomial Julia sets. Under revision. http://arxiv.org/abs/math.DS/0609044 On Yoccoz Return Functions. Available on ArXiv http://arxiv.org/abs/0908.3326


