I am a fourth year PhD student under the supervision of Professor John Smillie. I am interested in complex dynamics, in particular, the dynamics of complex Hénon maps.
Previously I studied my MMath at the University of Liverpool and undertook two projects supervised by Professor Mary Rees. These projects concerned the dynamics of quadratic polynomials.
With Professor Smillie I have been studying complex dynamics in two dimensions. We are developing a new notion of external rays for Hénon maps which can be computed in Mathematica. We hope to show these rays converge to the more traditional notion of external rays. Using these rays we are investigating the work of Chris Lipa and hope to develop that into a more rigorous theory.
This notion of external rays leads to approximations of the Hénon Julia set. We can take a projection of the data we generate and produce pictures. An early version of such a picture is shown below. On the left is a SaddleDrop output due to Sarah Koch and the right shows the Mathematica output. More examples can be found here.
Email: Thomas.Richards "at" warwick.ac.uk
Office: Room B3.04, Zeeman Building