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 meta-Fibonacci 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.
(Off-prints available upon request).
A Family of Meta-Fibonacci Sequences Defined by Variable-Order Recursions.
Journal of Integer Sequences, Volume 9, Issue 1, Article 06.1.8, 2006.
Return Times of Polynomials as meta-Fibonacci Numbers.
Conformal Geometry and Dynamics, Volume 12, October 2008.
Brownian motion, random walks on trees, and harmonic measure on polynomial Julia sets.
On Yoccoz Return Functions.
Available on ArXiv