Morphogenesis of gravitational structures through a non-differentiable approach

Abstract

Abstract. The present paper analyzes the morphogenesis of gravitational structures, assuming that dynamics of a test particle in a gravitational field takes place on continuous but non-differentiable curves. The dynamics of such gravitational system is described by an equation for a complex speed that characterizes its rheological behavior. Moreover, the separation of movements on interaction scales in the dynamics equation implies a non-differentiable hydrodynamical model. Finally, such an approach was applied both to one and two body problems and, via numerical simulation, to the morphogenesis of gravitational structures. Consequently, quantization at intragalactic (Solar System) and extragalactic scales (Tifft's effect) as well as certain modifications of Newton's force occur. At the same time there is a tendency to form gravitational structures at any epoch, without inflationary phase.