Preturbulence, Strange Attractors and Geometric Models

Abstract

We commence our study of the parameter region r > 13.926 by attempting to confirm the first of the two suggestions made at the end of the last chapter. We can use the computer to locate stable and non-stable periodic orbits. The techniques used are based on Newton1s method, are well known, and are described in Appendix E. To use the techniques it is necessary to have a reasonably good guess for the position and period of the orbit we wish to locate. Appendix E contains practical hints on how to come by such initial guesses, and on how to use the techniques. Appendix E also contains the description of a technique for following a periodic orbit with changing parameter.