Epstein Secrets

MARTIN,HARRIET G ELLIOT IV,WALTER J LORENTZEN,MATTHEW B GWYNNE,JAY M R H TRUST

ER HOLDER,DOUG A MYERS,JAMES DELANEY,KATHY RAMSING,BYRON L COOK,CYNTHIA

eer, George Birkoff (1922), was computing the output of a very reduced subset of Saltzman’s differential equations for predicting the weather (1962). Lorenz found that numerically integrated trajectories manifested unpredictable times and directions of motion between the two spiral orbits of what has come

ike tents, sine functions and parabolas can be extracted from and represent the behavior of higher dimensional, nonlinear differential equations (see Devaney, 1989; Schuster, 1989 or Moon, 1992 for intuitive descriptions). They varied a parameter, such as the height of the tent or parabola, to systematical

in dimension greater than two (for orbits to be more than a fixed point or limit cycle, able to snake around without necessarily intersecting ), the Lorenz attractor has dimension just a little over two, our difficulties with establishing the “true” physiological dimension of real biological observables

orbits recursively as the dynamics proceed; and (3) Indecomposability—the attractor is not separable into isolated regions and no points escape (see Devaney, 1989, for one of the clearest definitions). Of particular relevance to information encoding and transport by brain mechanisms, it is important to vi