DYNAMICS IN FRACTAL SPACES

à Lvaro G. Lã“pez
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à Lvaro G. Lã“pez: Nonlinear Dynamics, Chaos and Complex Systems Group, Departamento de Física, Universidad Rey Juan Carlos, Tulipán s/n, 28933 Móstoles, Madrid, Spain

FRACTALS (fractals), 2021, vol. 29, issue 01, 1-21

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

Keywords: Stochastic processes; fractal space; Langevin equation; nonlinear dynamics; fluctuations (search for similar items in EconPapers)
Date: 2021
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Persistent link: https://EconPapers.repec.org/RePEc:wsi:fracta:v:29:y:2021:i:01:n:s0218348x2150016x

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DOI: 10.1142/S0218348X2150016X

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