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http://hdl.handle.net/2445/109926
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 Polinomis Pertorbacions singulars (Matemàtica) Nombres complexos Holomorphic functions Bachelor's theses Differentiable dynamical systems Topological dynamics Polynomials 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 |
URI: | http://hdl.handle.net/2445/109926 |
Appears in Collections: | Treballs Finals de Grau (TFG) - Matemàtiques |
Files in This Item:
File | Description | Size | Format | |
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memoria.pdf | Memòria | 1.54 MB | Adobe PDF | View/Open |
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