A tool for studying Bers slices of punctured tori
by David Dumas

About Bear

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.


2007-12-31 - Bear version 0.9.7 released

This release includes bug fixes, code improvements, and a new module for computing McShane-type sums over the tree of Markov triples. Source and binary packages are available from the SourceForge project site.

2006-02-26 - Updated DEBs for 0.9.6

New Debian binary packages of Bear 0.9.6 for systems with GCC4 as the default compiler (e.g. the lastest Debian unstable) are now available on the SourceForge project site.

2005-08-13 - RPM and DEB package offerings expanded

Bear has always been available as a source code archive and as a binary package for Debian GNU/Linux. Starting with version 0.9.6, binary packages in RPM format for several popular RPM-based GNU/Linux distributions will be offered. Currently, RPMs for Fedora Core 2, 3, and 4 on the i386 platform are available. (Note: for Fedora Core 2, the required library HDF5 is not a standard package, but it can be obtained from MonkeyRPMs.) A source RPM that can be used to build RPMs for other distributions is also provided.

The Debian GNU/Linux package options have also been expanded. Packages of the 0.9.6 releae for Ubuntu GNU/Linux 4.1 ("Warty") on i386 and Debian GNU/Linux unstable ("sid") on AMD64 have been added; as before, a Debian GNU/Linux unstable ("sid") i386 package is available. The debian package control files have also been incorporated into the source tar archive, making it easy to produce DEB packages for other dpkg-based GNU/Linux distributions.

Bear source code and binary packages are available from the SourceForge project site.

2005-08-13 - Bear version 0.9.6 released

This is a bugfix release that includes further performance improvments resulting from the same trace normalization issue that was fixed in the 0.9.5 release.

The interpolation features of the 'bers2' module are now much more effective since convergence of the interpolation to the actual holonomy is now much faster. (It is often possible to reduce the computation time for a large Bers slice calulation by a factor of 5 or more.) In addition, memory requirements for the 'bers2' module have been significantly reduced, and performance has been improved.

The source distribution now includes the control files necessary to make both RPM and DEB binary packages of bear. The included RPM spec file is designed for use on the Fedora Core series of GNU/Linux distributions, but should work on other RPM-based distributions with little modification. The dpkg control files have been tested with Debian GNU/Linux unstable ("sid") and Ubuntu GNU/Linux 4.1 ("Warty"). As always, files are available from the SourceForge project site.

2005-07-11 - Bear version 0.9.5 released

This release is a minor patch against 0.9.4 to fix a numerically unstable part of the Bers slice holonomy calculation. This results in a drastic improvement in the stability and accuracy of Bers slice calculations.

2005-06-08 - Bear version 0.9.4 released

This is a bugfix release that includes minor feature enhancements. The build system has been improved, specifically addressing problems building on Darwin / Mac OS X, and compatibility with older versions of the HDF5 and GSL libraries. Overall the portability of the build system and source code has improved significantly, and this release builds successfully without any changes on these platforms (and probably many more): New features in this release include: As always, files are available from the SourceForge project site.

2005-03-24 - Bear version 0.9.3 released

This is the second release. New features in version 0.9.3 include support for several types of Schwarzian equation integration contours (splines, ellipses, piecewise linear paths), and a new module bers2 for computing holonomy on a sparse grid and then interpolating over a finer grid. An experimental module anosov for computing unstable manifolds of pseudo-anosov mapping classes was also added; while functional, it is still under active development and may change significantly in future releases. Several minor usability improvements were also made. All files are available from the SourceForge project site.

2004-06-12 - Bear version 0.9.0 released

This is the first release as a project. Version 0.9.0 includes support for the HDF5 output format, scripting using the Lua extension language, and minor improvements to the discreteness testing algorithm. Source, RPM, and DEB packages are available from the SourceForge project site.

2004-05-09 - Bear project created

Bear has just been accepted as a SourceForge project. We are in the process of moving project web pages and resources to their new home, and preparing a new release of the software.


Documentation & How-to

Building Bear from source

Compiling the source and installing Bear in a posix environment.

Installing Bear from a binary package

Including dependency problems, where to find packages for HDF5, GSL, etc.

Using Bear

Note: The manuals below were generated for Bear 0.9.4. An updated HTML manual for the latest release (0.9.7) will be available shortly.


Source and binary packages can be found on the SourceForge project site.


Development of this software was partially supported by a National Science Foundation Postdoctoral Research Fellowship (award 0402964). Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author and do not necessarily reflect the views of the National Science Foundation.


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