On turbulence: deciphering a renormalization flow out of an elliptic curve, II

Luis G. D. C. Borges

Published 2013-07-24Version 1

Reaching for a better understanding of turbulence, a line of investigation was followed, its main presupposition being that each scale dependent state, in a general renormalization flow, is a state that can be modeled using a class of ninth degree polynomials. These polynomials are deduced from the Weierstrass models of a certain kind of elliptic curves. As the consequences of this presupposition unfolded, leading to the numerical study of a few samples of elliptic curves, the L functions associated with these later were considered. Their bifurcation diagrams were observed and their escape rates were determined. The consistency of such an approach was put to a statistical test, measuring the rank correlation between escape rates and values taken by these L functions on the point z=1+0i. In the most significant case, the rank correlation coefficient found, r_s, was about r_s=-0.78, with an associated p-value of an order of magnitude close to the (-69) power of 10.