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 Q₁ and Q₀ 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 R³ 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 Q₁ and Q₀, 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.