DYNAMICS IN FRACTAL SPACES

We study the dynamics of a particle in space that is non-differentiable. Non-smooth geometrical objects have an inherently probabilistic nature and, consequently, introduce stochasticity motion body lives their realm. use mathematical concept fiber bundle to characterize multivalued geodesic trajectories going through point Then, we generalize our concepts everywhere non-smooth structures. The resulting theoretical framework can be considered hybridization theory surfaces and stochastic processes. keep as general possible, order allow for introduction other fundamental processes capable modeling fractality or fluctuations any conceivable continuous, but non-differentiable space.