Fagella Rabionet, NúriaRodríguez Reverter, Àlex2022-04-132022-04-132021-06-20https://hdl.handle.net/2445/184944Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2021, Director: Núria Fagella Rabionet[en] In this project we analyze the behavior of transcendental functions under iteration i.e., those with an essential singularity at $\infty$. We emphasize the general case of meromorphic transcendental functions with the aim of understanding the dynamical consequences of the presence of poles. Finally, we apply these results and techniques to study, on the one hand, the dynamics of the exponential family $E_{\lambda}(z)=\lambda e^{z}$, and on the other hand, the family of meromorphic maps $$ f_{\lambda}(z)=\lambda\left(\frac{e^{z}}{z+1}-1\right). $$ In this last part, which is original work, we prove that under certain conditions, the basin of attraction of $z=0$ is infinitely connected.80 p.application/pdfengcc-by-nc-nd (c) Àlex Rodríguez Reverter, 2021http://creativecommons.org/licenses/by-nc-nd/3.0/es/Sistemes dinàmics complexosTreballs de fi de grauFuncions transcendentsFuncions meromorfesFuncions de variables complexesComplex dynamical systemsBachelor's thesesTranscendental functionsMeromorphic functionsFunctions of complex variablesinfo:eu-repo/semantics/bachelorThesisinfo:eu-repo/semantics/openAccess