The progress on chaos made at UGA was not by design, but by some happenstance in circumstances, tales of which will be woven into this talk. The technical details are as follows:
The clearest definition of chaos is given by Sharkovskii's theorem, which says that the existence of a 3-cycle in a chaotic map implies chaos. Thus showing a 3-cycle exists is of deepest interest. For the logistic map I have solved the 3-cycle problem[1,2]. At the fully developed chaos I have also proved that the trajectories are ergodic as well by a concept from measure theory. The same conclusion is reached by my ergometric theory[3].
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1. M H Lee, J Math Phys 50, 1227 (2009).
2. M H Lee, Acta Phys Pol B 42, 1071 (2011).
3. M H Lee, Phys Rev Lett 87, 250601 (2001).
