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Title: Iteration of holomorphic functions in the complex plane
Author: Millán Carrasco, Albert
Director/Tutor: Fagella Rabionet, Núria
Keywords: Funcions holomorfes
Treballs de fi de grau
Sistemes dinàmics diferenciables
Dinàmica topològica
Pertorbacions singulars (Matemàtica)
Nombres complexos
Holomorphic functions
Bachelor's thesis
Differentiable dynamical systems
Topological dynamics
Singular perturbations (Mathematics)
Complex numbers
Issue Date: 27-Jun-2016
Abstract: When a holomorphic function is iterated, it generates a dynamic system on the complex plane. In this project, we describe both the local and global behavior of the different orbits of a rational map on the complex plane (or the Riemann sphere). We mainly concentrate in the study of the dynamical plane (where initial conditions and orbits live) although we briefly discuss one parameter families of polynomials and their bifurcation loci, like the well known Mandelbrot set. Towards the end, we experiment with a singular perturbation of a family of cubic polynomials and explore the drastic changes that occur in the topology of their Julia sets.
Note: Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2016, Director: Núria Fagella Rabionet
Appears in Collections:Treballs Finals de Grau (TFG) - Matemàtiques

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