论文标题
分形空间的动力学
Dynamics in fractal spaces
论文作者
论文摘要
我们研究粒子在不可差异的空间中的动力学。非平滑的几何物体具有固有的概率性质，因此，在生活在其领域的身体运动中引入了随机性。我们使用纤维捆绑包的数学概念来表征经过一个不可差异点的地理轨迹的多价性质。然后，我们将概念推广到任何地方的非平滑结构。所得的理论框架可以视为表面理论和随机过程理论的杂交。我们将这些概念保持尽可能笼统，以允许引入其他基本过程，能够建模任何可能的连续但不可差的空间的分形或波动的波动。
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.
