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tfg_pascual_roig_marc.pdf (2.04 MB)

Document type

Bachelor thesis

Publication date

2023-02-24

Publication license

cc-by-nc-nd (c) Marc Pascual Roig, 2023
Please use this identifier to cite or link to this item: https://hdl.handle.net/2445/198920

Circle maps and the Arnold family

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Abstract

[en] As a dynamical system, the Arnold Family of circle maps is itself a source of many curious and particular results and phenomena. The main goal of this work is to explain and classify the possible dynamics of the family while encountering these special occurrences. In order to view and deeply understand the origin behind all the dynamical events that are occurring, we begin by setting a complete background on circle homeomorphisms. We later make use of the complexification tool and complex dynamics so we not only complete our discussion, but we extend it. Actually, we see the dynamics in the whole complex plane, and with the aid of some programs we provide a visual representation of it.

Description

Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2023, Director: Núria Fagella Rabionet

Subject

Funcions meromorfes, Treballs de fi de grau, Funcions de variables complexes, Sistemes dinàmics de baixa dimensió, Sistemes dinàmics complexos

Subject (English)

Meromorphic functions, Bachelor's theses, Functions of complex variables, Low-dimensional dynamical systems, Complex dynamical systems

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Treballs Finals de Grau (TFG) - Matemàtiques

Citation

PASCUAL ROIG, Marc. Circle maps and the Arnold family. [consulted: 13 of August of 2026]. Available at: https://hdl.handle.net/2445/198920

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