*
Last changed Wed Aug 29 13:31:01 BST 2001
We are grateful to David Wright who produced a number of pictures
in connection with our paper * inserttitle
.

The Trace slice

For downloading, the source of this document is in

These correspond to traces

(using the upper case convention for inverses).

We use a boundary tracing method for exploring the values of for
which such a group is discrete. The *p*/*q* word in *a*
and *b* is defined by

We solve in order of *p*/*q* for values of
where *w _{p}*

The resulting plot of is below, for cusps ranging from -3/1 just off to the left to 3/1 just off to the right.

epstein-lset.epsi is a large file (around 30Mb). The advantage of taking a look at
it with a PostScript viewer, like ghostscript or gv, is that David
Wright's program computes the limit set in circular order. The limit
set is naturally the continuous image of a circle. In the viewer, the
picture appears comparatively slowly, and you see a movie of the image in the
plane of a point on the circle. This enables one to see the map,
rather than just the image of the map.