Generation of fractals as Duffing equation orbits

Date

2019-05-01

Author

Akhmet, Marat
Fen, Mehmet Onur
Alejaily, Ejaily Milad

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This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

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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.

Subject Keywords

Mathematical Physics, General Physics and Astronomy, Applied Mathematics, Statistical and Nonlinear Physics

URI

https://hdl.handle.net/11511/35744

Collections

Department of Mathematics, Article