Mauro, Thanks for pointing me to the analysis work of Mathis. At present, I don't know if I can make practical use of his mathematical findings or not. It's probably going to make my brain hurt for quite a spell while attempting to get the gist of it all.
To clarify what I have been doing: For several years now I have been researching what I have assumed is probably considered by most an uninteresting aspect of Newtonian based Celestial Mechanics, (CM). More to the point, I have focused primarily on computational feed-back loops where chaos is introduced into the solution. I've been plotting the "chaotic" results for some time now. No doubt, much of this work is related to emergent behavior, fractals, and what-not. It would not surprise me if some of Wolfram's work may have occasionally touched on what I have been studying. (Mike Carroll brought Worlfram's work to my attention.) Serendipitously, I recently discovered that Wolfram used his Mathematica software to study the characteristics of the empty foci belonging to a classic elliptical shaped satellite/planetary orbit. I was gratified to discover that the results Wolfram's Mathematica produced seemed to mirror some of my own independently researched findings. I have assumed (perhaps incorrectly) that the specific CM branch I'm studying (the chaotic aspect) is probably considered uninteresting and not of much practical value to most scientists & researchers. I assume so because of the fact that when it comes to accurately plotting the orbits of celestial bodies like planets, moons, and satellites the last thing one wants to do is introduce the effects of chaos into the algorithm! For obvious reasons the effects of chaos must be kept at a minimum in order to accurately plot a future position of a celestial body. This is accomplished by making sure the computational iterative samples one feeds into the algorithm are sufficiently small, from plotted point to the next plotted point. Things can quickly get squirrely as one's "satellite" approaches the main attractor body, and the plotted point-to-point positions increase in distance from each other geometrically. But there by the Grace of God go I. I've discovered that within the unpredictable realms of chaos a wealth of strange and weird-like behavior is worth exploring. At the razor's edge, where the boundary between Order and Chaos meet, I find tantalizing behavior. My chaotic research continues. I hope to eventually put some of my findings out on the net. Much more work needs to be done... It's daunting. Regards Steven Vincent Johnson www.OrionWorks.com www.zazzle.com/orionworks
