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Chris Zeeman named a normal factor. It is the smooth growth of the material wave of mesodermal (to become muscle, connective tissue and bone) tissue. Zeeman called the front to back dimensional gradient of influence, the secondary wave of adhesiveness, the splitting factor. The value of this secondary wav
e impressions of others can arise quickly and from only a few data points of observation. In the late 1960’s, University of California mathematician, Rufus Bowen, proved the now famous shadow theorem. This says that in dynamical states of hyperbolicity, directly observable on the screen in computer simulations
ally-relevant analog computer discoveries about the Van der Pol and comparable periodically forced, dissipative (energy utilizing) Duffing equations (Zeeman, 1976) were made in the early 1960’s by electrical engineer, Yoshi Ueda (1992), but his thesis director, Chihiro Hayashi of Japan’s Kyoto University,
1968), the French mathematicians, Rene Thom (1972) and David Ruelle (1978) and the U.C. Berkeley mathematicians, Steve Smale (1967) and his student, Rufus Bowen (1975), and their associates who gathered together these and other related computational discoveries and embedded them in a qualitative theory of non
of graphic representations of their geometric and topological forms. Notably successful examples can be found in the work of Thom, Arnold (1984) and Zeeman (1977), who were inspired by “caustics” (the shapes made on surfaces by the coincidence of reflected or refracted light rays) and Whitney’s represent
y, R.M. (1990) Nonlinear forcasting as a way of distinguishing chaos from measurement error in time series. Nature 344:734-741. Sullivan, D. (1979) Rufus Bowen. Publ. Math. |.H.E.S. 50:255 Szeto, H.H., Cheng, P.Y., Decena, J.A., Cheng, Y., Wu, D., Dwyer, G. (1992) Fractal properties in fetal breathing dynam
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