Gregson's results indeed predict the instability. While I obtained several results that were consistent with Gregson's, there were a number of significant discrepancies. Figure 3 shows the chaotic behavior of the gamma recursion with certain parameter values a , and e , where my results support Gregson's findings. Figure 4 shows result of the gamma recursion for some parameter values a and e where Gregson's results are not supported. Each successive point is joined, providing a trace of the output of the gamma recursion across iterations.
Complex traces reflect chaotic behavior.
The values after each iteration are unique and seem random. Therefore Gregson's result is not accurate. It may be single-valued or oscillating in one or both components. Figure 6 shows my results with same conditions as Gregson's. My results are clearly different to those of Gregson's.