The standard problem in the topological analysis of experimental chaotic systems is to determine the simplest branched manifold (``template'') that can hold a set of periodic orbits extracted from the time series and embedded in a phase space. By definition, orbits can be projected to the surface of the template without modifying their topological invariants (linking numbers, torsions, etc...). Accordingly, the solution of the standard problem depends only on these topological invariants.
The libtop software package provides programs for determining the simplest templates compatible with a user-provided list of topological invariants. For example, orbcomb is a program that finds the template given the topological invariants, while findnames can find possible symbolic names for the orbits if you feed it with topological invariants and the template found by orbcomb.
When fed with the list of topological invariants and with the output of orbcomb and findnames, the part program determines an approximation to a generating partition using the symbolic dynamical information contained in topogical invariants (see Plumecoq and Lefranc, Physica D 144 , 231-258 (2000) and Physica D 144 , 259-278 (2000) ). Here you can find an example of ultra-high resolution partition obtained with orbcomb, findnames and part. This example was studied specifically to show that topological analysis is valid down to very small scales. For most purposes, requirements are more modest, and this method can be applied to experimental systems (see Lefranc et al., Phys. Rev. Lett. 73, 1364-1367 (1994)).
These programs call routines from a C++ library implementing objects such as symbolic names, templates (called KnotHolder because template is a keyword), invariants, etc. This package has been mostly written my Marc Lefranc, with a few contributions by Jérôme Plumecoq.
Unfortunately, documentation leaves to be desired at this stage, which makes it a bit difficult to use. However, you can find below the man pages of programs orbcomb and findnames as well as of the libtop library, which should be enough to get you started. Please do not hesitate to ask questions to Marc Lefranc if anything is unclear. The gaps in the documentation will be filled with the replys to your questions. When documentation will appear to be satisfactory, the version number of the package will be bumped to 1.0.
Man pages: orbcomb.man findnames.man libtop.man
See also the libtop.txt and part.txt files that are included in the doc directory of the source tree.
Bug reports as well as enhancement requests, or more generally any type of feedback, are welcome!
Here is the source code, as a gziped unix tar archive: libtop-0.99.8.tar.gz. It is mainly
developed on Red Hat Linux, but should compile on a number of other
Unices (it has also been used on HP-UX and DEC/OSF1). On a rpm-based
linux distribution, you can build a binary rpm package with the
command
OSTYPE=linux-gnu rpmbuild -ta libtop-0.99.8.tar.gz
On a Debian system, use rpm to build the rpm package and then alien to
convert it to a .deb package.
Important notice : If you find these programs useful
and if you use them in a research paper, please be kind enough to
cite:
and to put a pointer to this site so that others can find it. Thank
you !
