Self-Structuring Of Cellular And Channel Type In Complex System Dynamics In The Framework Of Scale Relativity Theory

In the framework of Scale Relativity Theory, by analyzing dynamics of complex system structural units based on multifractal curves, both Schrodinger and Madelung approaches are functional and complementary. The Madelung selected approach involve synchronous modes through SL(2R) transformation group based on a hidden symmetry. Moreover, coherence domains through Riemann Manifolds embedded with a Poincare metric based on a parallel transport of direction, in a Levi Civita sense are presented. In this last context, stationary-non-stationary dynamics transition through harmonic mapping from the usual space to the hyperbolic one is manifested as cellular and channel type self-structuring.