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memoria.pdf (1.5 MB)

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Bachelor thesis

Publication date

2016-06-27

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cc-by-nc-nd (c) Albert Millán Carrasco
Please use this identifier to cite or link to this item: https://hdl.handle.net/2445/109926

Iteration of holomorphic functions in the complex plane

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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.

Description

Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2016, Director: Núria Fagella Rabionet

Subject

Funcions holomorfes, Treballs de fi de grau, Sistemes dinàmics diferenciables, Dinàmica topològica, Polinomis, Pertorbacions singulars (Matemàtica), Nombres complexos

Subject (English)

Holomorphic functions, Bachelor's theses, Differentiable dynamical systems, Topological dynamics, Polynomials, Singular perturbations (Mathematics), Complex numbers

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Treballs Finals de Grau (TFG) - Matemàtiques

Citation

MILLÁN CARRASCO, Albert. Iteration of holomorphic functions in the complex plane. [consulted: 6 of June of 2026]. Available at: https://hdl.handle.net/2445/109926

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