Bear is a tool for studying Bers slices of punctured tori.
Bear is a mathematical research tool for calculating and testing discreteness of holonomy representations of complex projective structures on punctured tori. It can be used to draw pictures of Bers slices and explore the geometry of quasifuchsian space in the SL2(C) representation variety. It also has powerful scripting features that make it easy to create complex animations or to automate larger calculations.
Bear computes holonomy by applying standard ODE integration techniques to the Schwarzian differential equation; currently it uses an ODE solver from the GNU Scientific Library (GSL). The discreteness testing module in Bear includes the first implementation of a discreteness algorithm for punctured torus groups based on the paper Markoff triples and quasifuchsian groups by Brian Bowditch, published in Proc. London. Math. Soc. 77 (1998) 697--736.
What's New in This Release:
· This release includes bugfixes, code improvements, and a new module for computing McShane-type sums over the tree of Markov triples.