Dynamics for chaos and fractals

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2019

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Alejaily, Ejaily

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In this thesis, we study how to construct and analyze dynamics for chaos and fractals. After the introductory chapter, we discuss in the second chapter the chaotic behavior of hydrosphere parameters and their influence on global weather and climate. For this purpose, we investigate the nature and source of unpredictability in the dynamics of sea surface temperature. The impact of sea surface temperature variability on the global climate is clear during some global climate patterns like the El Niño-Southern Oscillation. The interactions between these types of global climate patterns may transmit chaos. We discuss the unpredictability as a global phenomenon through extension of chaos horizontally and vertically by using theoretical as well as numerical analyses. In the third chapter, we introduce a technique concerning the construction of dynamics for fractals. Deterministic fractals like Julia sets are crucial for understanding the fractal phenomenon. These structures are deterministically arising from simple dynamics of iteration of analytic functions. On the basis of the dynamics, we develop a scheme to map fractals through iterations. This allows to involve fractals as states of dynamical systems as well as to introduce dynamics in fractals through differential and discrete equations. Creation of effective frameworks for applications of fractals and assisting to explore the relationship between fractals and chaos by the involvement of dynamics in fractals are important aspects in this direction.

Subject Keywords

Fractals., Chaos, Ocean–atmosphere interaction, El Niño-southern oscillation, Sea surface temperature, Vallis model, Lorenz system, Advection equation, Global weather unpredictability, Fractals, Julia set, Mandelbrot set, Fatou-Julia iteration, Sierpinski fractals, Fractal mappings, Discrete and continuous fractal dynamics, Duffing equation, Van der Pol equation

URI

http://etd.lib.metu.edu.tr/upload/12623664/index.pdf
https://hdl.handle.net/11511/45432

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Graduate School of Natural and Applied Sciences, Thesis

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Citation Formats

E. Alejaily, “Dynamics for chaos and fractals,” Thesis (Ph.D.) -- Graduate School of Natural and Applied Sciences. Mathematics., Middle East Technical University, 2019.