DYNAMICAL SYSTEMS FOR RATIONAL FUNCTIONS
Ключевые слова:
Keywords: Dynamical systems, rational functions, Julia set, Fatou set, complex dynamics, periodic points, Riemann sphere, bifurcation, fractals, iteration theory.Аннотация
Annotation: This article explores the theory and application of dynamical systems generated by rational functions. The study focuses on the iteration of rational functions on the Riemann sphere, key concepts such as Julia and Fatou sets, stability of periodic points, and applications in complex dynamics and fractal geometry. The article synthesizes modern literature, highlights computational methods, and presents results on system behavior under different rational mappings. It also discusses theoretical implications and potential avenues for future research in mathematics and applied sciences.
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