Fagella Rabionet, NúriaNúñez Corbacho, Joan2024-05-222024-05-222024-01-17https://hdl.handle.net/2445/211660Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2024, Director: Núria Fagella Rabionet[en] The aim of this project is to characterise the dynamics of finite Blaschke products, which are precisely the proper maps of the unit disk. It is proven that, inside the unit disk, all points converge to a unique point, the Wolff-Denjoy point. We build a classification of finite Blaschke products according to the position of the Wolff-Denjoy point and the dynamics around it. Finally, we study the restriction of finite Blaschke products to the unit circle and calculate explicitly a conjugacy to $z^d$. We end this work by showing a brief example of generalised Blaschke products, a nuanced variation of the previous family that presents rich dynamical phenomena, such as the emergence of Herman rings.69 p.application/pdfengcc-by-nc-nd (c) Joan Núñez Corbacho, 2024http://creativecommons.org/licenses/by-nc-nd/3.0/es/Funcions de variables complexesSistemes dinàmics complexosDinàmica topològicaTreballs de fi de grauFunctions of complex variablesComplex dynamical systemsTopological dynamicsBachelor's thesesinfo:eu-repo/semantics/bachelorThesisinfo:eu-repo/semantics/openAccess