Papers

Quasiregular dynamics

thesamovar — Mon, 31 May 2010 12:47:44 +0100

With Alastair Fletcher, I wrote some code for producing images of Mandelbrot and Julia sets for quasiregular mappings. A paper on this is currently in review, and can be accessed from arxiv.org. The code used to generate the images can be downloaded from the zip file below, including a description of how it works. The code requires Python 2.5/6 and Numpy.

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qr_dynamics.zip	8.78 KB

The twisting boundary of the Maskit slice

thesamovar — Wed, 22 Nov 2006 05:36:31 +0000

I am currently working on a paper, based on chapter 5 of my thesis, which I intend to submit to the journal Experimental Mathematics. This paper will present the numerical evidence I gathered during my PhD for the conjectures that the boundary of the Maskit slice is twisting (spiralling infinitely) almost everywhere, and has Hausdorff dimension less than 1.25.

You can download the current version as a PDF (~0.5MB).

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twisting.pdf	511.25 KB

Spirals in the boundary of quasifuchsian space

thesamovar — Sun, 15 Oct 2006 04:12:40 +0100

My paper Spirals in the boundary of slices of quasifuchsian space was published by the Journal of Conformal Geometry and Dynamics. The abstract reads:

We prove that the Bers and Maskit slices of the quasifuchsian space of a once punctured torus have a dense, uncountable set of points in their boundaries about which the boundary spirals infinitely.

You can download my version (slightly different to the published version) in PDF format (340k).

Below is a series of zooms into the Maskit slice, clockwise from top left to bottom right, illustrating the phenomenon of spirals in the boundary of the Maskit slice.

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spirals.pdf	339.63 KB