Lorenz Type Behaviors Associated To Fractal-Non-Fractal Transition In The Dynamics Of The Complex Systems

In the framework of Fractal Theory of Motion for the Scale Relativity Theory with arbitrary and constant fractal dimensions, dynamics in complex systems associated to the fractal-non-fractal transition are analyzed. Working with the assumption that these dynamics are described by means of fractal curves, Lorenz type behaviors become "operational" through a Galerkin method. Then Rayleigh and Prandtl effective numbers are specified both by means of classical kinetic coefficients and scale resolution while the dynamics variables act as the limit of a family of mathematical functions, non-differentiable for non-null scale resolution.