Multifario

Multifario is a set of subroutines and data structures for computing manifolds that occur in Dynamical Systems. Fixed points, periodic orbits, heteroclinic and homoclinic connections, and many types of singular motions have been formulated as solutions of systems of parameterized algebraic or two point boundary value problems. (See the set of objects which can be computed with AUTO.)

The code is structured so that the user can provide their own solvers, but two stand-alone solvers are provided. Both use the Lapack linear equation solvers (not distributed through COIN, available through Netlib). The first solver is for algebraic systems, the second is for two point boundary value problems, using a fixed mesh and Keller's Box scheme.

Interfaces to AUTO, (a full package for algebraic and two point boundary value problems), and LOCA (Sandia's continuation code) are available.

The output of the code is a "plotfile" and/or "centerfile", or an "atlas". The plotfile is a list of polyhedra which cover the manifold, whose vertices are have been projected via a routine the user may provide. The centerfile is a list of the points on the manifold at the center of each polyhedron. The atlas is a full dump of the data structure which the algorithm uses.

Basic conversion utilities are included for converting plotfiles to DataExplorer format, and to POV-RAY files. In addition a simple z-buffer code is included which will render a plotfile to a Tiff file, if the LIBTIFF library (not distributed through COIN) is available, or Postscript.