Motion Dynamic Scenarios in the Scale Relativity Theory

Abstract Assuming that any complex system, both structural and functional, can be assimilated to a mathematical object of multifractal type, it is shown that its dynamics can be described by multifractal curves. In such a framework, based on the Multifractal Theory of Motion, the Schrödinger multifractal and the Madelung multifractal scenarios become not only compatible, but also complementary in the dynamic descriptions.