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table. Rigid things can more easily fracture. The rich, altered states of consciousness that emerge whil
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
stical measures, Hr, Hu, AC and srs? The yield is rich and unexpected. We find an enjoining of values of
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
ron was by Gerstein and Mandelbrot (1964). Though rich with possibilities, it has been only very recentl
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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