Please use this identifier to cite or link to this item: https://hdl.handle.net/2445/198332
Title: Topological structures in complex dynamics
Author: Ayadi Antón, Ayla
Director/Tutor: Fagella Rabionet, Núria
Keywords: Sistemes dinàmics complexos
Treballs de fi de grau
Equacions funcionals
Funcions holomorfes
Fractals
Complex dynamical systems
Bachelor's theses
Functional equations
Holomorphic functions
Issue Date: 24-Jan-2023
Abstract: [en] Many sets in the field of planar topology are considered "exotic" and not frequently encountered in everyday life. However, these sets possess unique and intriguing topological properties, and quite often also a visually appealing aesthetic. In recent years, thanks to the resurgence of complex dynamics, many of these exotic sets have been found to be Julia sets for complex analytic functions. In this work, we delve into the world of planar topology, provide an overview of the basics of complex dynamics, and present four examples of such sets: den- drites, Cantor sets, Sierpiński curves, and Cantor bouquets. To conclude, we also explain how these sets arise through specific families of complex maps, such as the quadratic family, the complex exponential family, and a certain type of singularly perturbed rational maps.
Note: Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2023, Director: Núria Fagella Rabionet
URI: https://hdl.handle.net/2445/198332
Appears in Collections:Treballs Finals de Grau (TFG) - Matemàtiques

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