The Database software represents
a large effort to develop efficient algorithms
and data structures to obtain mathematically
rigorous global representations of the dynamics
of mutiparameter dynamical systems. This
includes the ability to use algebraic
topological invariants to describe the dynamics
and tools to interpret the resulting output
which in itself can take the form of rather
large data sets.

The different topological tools as well as details on how the computations are being carried out can be found in this survey

.