==== Generating Data ====

I followed the first couple steps of John G's howto essentially verbatim and deviated only with respect to calculation of the poincare section.

I used the following script file, with eigenvalues already present, to generate my data:

  #!/bin/bash
  #This will hopefully generate all of the data I need to construct a poincare section of 
  # the upper branch unstable manifold.
  
  addfields 1 UB 1.12670e-05 e0 eq2_1
  addfields 1 UB 1.26960e-05 e0 eq2_2
  addfields 1 UB 1.43072e-05 e0 eq2_3
  addfields 1 UB 1.61215e-05 e0 eq2_4
  addfields 1 UB 1.81659e-05 e0 eq2_5
  addfields 1 UB 2.04695e-05 e0 eq2_6
  addfields 1 UB 2.30653e-05 e0 eq2_7
  addfields 1 UB 2.59902e-05 e0 eq2_8
  addfields 1 UB 2.92860e-05 e0 eq2_9
  addfields 1 UB 3.29998e-05 e0 eq2_10
  addfields 1 UB 3.71846e-05 e0 eq2_11
  addfields 1 UB 4.19000e-05 e0 eq2_12
  addfields 1 UB 4.72134e-05 e0 eq2_13
  addfields 1 UB 5.52006e-05 e0 eq2_14
  addfields 1 UB 5.99470e-05 e0 eq2_15
  addfields 1 UB 6.75490e-05 e0 eq2_16
  
  for i in eq2_*.ff ; do tag=${i#eq2_} ; couette -T0 0 -T1 400 -o data-${tag%.ff} $i ; done

I then created a parameter dependent flow field, that mixed two fields, or equivalently, john's e_theta.

<latex>
e_{\theta} = sin(\theta)\vec{u}_0 + cos(\theta)\vec{u}_1
</latex>

I set theta to be pi/4, to get the strongest possible contribution from both fields.  I then used poincare.cpp to calculate the intersections of each of the trajectories calculated in the script and saved them to disk.  I then plotted them, and what resulted is what is in my blog.