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Please use this identifier to cite or link to this item: https://hdl.handle.net/2445/220415
Propietats i dimensió de Hausdorff de conjunts de Julia polinomials
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L’objectiu d’aquest treball de final de grau és entendre algunes propietats dels conjunts de Julia polinomials aixı́ com la noció de dimensió de Hausdorff, molt associada a la geometria fractal. En concret, aprofitarem el marc teòric dels IFS per a donar una aproximació asimptòtica de la dimensió de Hausdorff dels conjunts de Julia que siguin de Cantor. Treballarem també amb el conjunt de Multibrot, demostrant la dicotomia fonamental i donant resultats sobre la seva component principal.
The objective of this final degree project is to understand some properties of polynomial Julia sets, as well as to understand the notion of Hausdorff dimension, which is highly related to fractal geometry. Specifically, we will use the theoretical mark of the iterated function systems to give an asymptotic approximation of the dimension of Cantor-like Julia sets. We will also work on the Multibrot set, demonstrating the fundamental dichotomy and giving results for its principal component.
The objective of this final degree project is to understand some properties of polynomial Julia sets, as well as to understand the notion of Hausdorff dimension, which is highly related to fractal geometry. Specifically, we will use the theoretical mark of the iterated function systems to give an asymptotic approximation of the dimension of Cantor-like Julia sets. We will also work on the Multibrot set, demonstrating the fundamental dichotomy and giving results for its principal component.
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Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2024, Director: Núria Fagella Rabionet
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ROS LÓPEZ, Àngel. Propietats i dimensió de Hausdorff de conjunts de Julia polinomials. [consulted: 7 of October of 2026]. Available at: https://hdl.handle.net/2445/220415