Akhmet Marat, Fen Mehmet Onur, Alejaily Ejaily Milad
Department of Mathematics, Middle East Technical University, 06800 Ankara, Turkey.
Department of Mathematics, TED University, 06420 Ankara, Turkey.
Chaos. 2019 May;29(5):053113. doi: 10.1063/1.5087760.
Dynamics are constructed for fractals utilizing the motion associated with Duffing equation. Using the paradigm of Fatou-Julia iteration, we develop iterations to map fractals accompanied with a criterion to ensure that the image is again a fractal. Because of the close link between mappings, differential equations and dynamical systems, one can introduce dynamics for fractals through differential equations such that they become points of the solution trajectory. There is no doubt that the differential equations have a distinct role for studying chaos. Therefore, characterization of fractals as trajectory points is an important step toward a better understanding of the link between chaos and fractal geometry. Moreover, it would be helpful to enhance and widen the scope of their applications in physics and engineering.
利用与达芬方程相关的运动为分形构建动力学。使用法图 - 朱利亚迭代范式，我们开发迭代以映射分形，并伴有一个准则以确保图像再次是分形。由于映射、微分方程和动力系统之间的紧密联系，可以通过微分方程为分形引入动力学，使得它们成为解轨迹的点。毫无疑问，微分方程在研究混沌方面具有独特作用。因此，将分形表征为轨迹点是朝着更好地理解混沌与分形几何之间联系迈出的重要一步。此外，这将有助于增强和拓宽它们在物理和工程中的应用范围。
