Oct 19 2003 since the original version of the project http://cns.physics.gatech.edu/ChaosBook/projects/variational.ps.gz Yueheng Lan has made quite a bit of progress, see the two papers on "Periodic orbit extraction", http://cns.physics.gatech.edu/~predrag/papers/preprPOT.html#POextract You might want to have a look at them. The way Lan solved the problem is not necessarily the only way - for example, finite damping of a Newton step suffices, infinitesimal Newton steps are probably too cautious. Feel free to follow your own path - the two papers will give you some idea about what has been done, and what the related literature is. P Cvitanovic'