Towards a Holographic-Type Perspective in the Analysis of Complex-System Dynamics

Abstract

By operating with the Scale Relativity Theory by means of two scenarios (Schrӧdinger and Madelung-type scenarios) in the dynamics of complex systems, we can achieve a description of these complex systems through a holographic-type perspective. Then, a gauge invariance of the Riccati type becomes functional in complex-system dynamics, which implies several consequences: conservation laws (in particular, for dynamics, the kinetic momentum conservation law), simultaneity and synchronization among the structural units’ (belonging to a complex system) dynamics, and temporal patterns through harmonic mappings. Finally, an economic case analysis is highlighted.

Keywords

• Scale Relativity Theory
• Schrödinger-type scenario
• Madelung-type scenario
• SL(2R) group
• harmonic mappings
• fractal