Agop Maricel, Gavriluț Alina, Grigoraș-Ichim Claudia, Toma Ștefan, Petrescu Tudor-Cristian, Irimiciuc Ștefan Andrei
Department of Physics, "Gh. Asachi" Technical University of Iasi, 700050 Iasi, Romania.
Romanian Scientists Academy, 54 Splaiul Independentei, 050094 Bucharest, Romania.
Entropy (Basel). 2020 Sep 4;22(9):987. doi: 10.3390/e22090987.
In a multifractal paradigm of motion, Shannon's information functionality of a minimization principle induces multifractal-type Newtonian behaviors. The analysis of these behaviors through motion geodesics shows the fact that the center of the Newtonian-type multifractal force is different from the center of the multifractal trajectory. The measure of this difference is given by the eccentricity, which depends on the initial conditions. In such a context, the eccentricities' geometry becomes, through the Cayley-Klein metric principle, the Lobachevsky plane geometry. Then, harmonic mappings between the usual space and the Lobachevsky plane in a Poincaré metric can become operational, a situation in which the Ernst potential of general relativity acquires a classical nature. Moreover, the Newtonian-type multifractal dynamics, perceived and described in a multifractal paradigm of motion, becomes a local manifestation of the gravitational field of general relativity.
在运动的多重分形范式中，香农最小化原理的信息功能引发了多重分形类型的牛顿行为。通过运动测地线对这些行为的分析表明，牛顿型多重分形力的中心与多重分形轨迹的中心不同。这种差异的度量由偏心率给出，它取决于初始条件。在这种情况下，通过凯莱 - 克莱因度量原理，偏心率的几何形状成为罗巴切夫斯基平面几何。然后，在庞加莱度量下，通常空间与罗巴切夫斯基平面之间的调和映射可以变得可操作，在这种情况下，广义相对论的恩斯特势具有经典性质。此外，在运动的多重分形范式中所感知和描述的牛顿型多重分形动力学，成为广义相对论引力场的一种局部表现。
