# Unstable Periodic Trajectories

This Web page contains the data referred to in the paper
*Topological-numerical approach to the existence
of periodic trajectories in ODEs* by Pawel Pilarczyk.
Please, consult this paper for explanation of the data files
available below.

The compressed archive
r31pair.zip (3.8 MB, DOS format)
contains the sets *Q*_{1} and *Q*_{0}
constructed for the unstable periodic trajectory
observed in the Rösser equations for *a* = 3.1.
The triples of numbers listed in the files *q1.cub* and *q0.cub*
represent the coordinates of the minimal corners of cubes
contained in corresponding sets.
The represented sets in *R*^{3} should be rescaled
by the factor of 1/128 to obtain the actual index pair.

The compressed archive
r31map.zip (12 MB, DOS format)
contains the enclosure of the analyzed map. This is a multivalued map
that defines an enclosure of the translation map by the time 3 under the flow.
The image of each box defined by its two opposite corners
is rigorously proved to be contained
in the corresponding box listed in the file.
Like in the definition of the sets
*Q*_{1} and *Q*_{0},
one needs to rescale the data by the factor of 1/128 to obtain the actual map.

For the computation of the homological Conley index,
the author used his own software which is publically available
at the CHomP website.

If you have any questions or remarks,
you are welcome to contact the author of the paper by e-mail.