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memoria.pdf (4.75 MB)

Document type

Bachelor thesis

Publication date

2014-09-13

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cc-by-sa (c) Jieyao Song, 2014
Please use this identifier to cite or link to this item: https://hdl.handle.net/2445/63023

On the local and global phase portrait of the 1-dimensional complex equation $z{\dot}= f (z)$

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Abstract

This work consists of studying the complex first order differential equation $z{\dot} = \dfrac{dz}{dt}=f(z),\hspace{2cm} z \in\mathbb{C},t\in\mathbb{R}$ where $f$ is an analytic function of $C$ except, possibly, at isolated singularities. This is a rather general family of complex functions that includes polynomial, rational, holomorphic and entire functions, and functions with isolated essential singularities.

Description

Treballs finals del Màster en Matemàtica Avançada, Facultat de matemàtiques, Universitat de Barcelona, Any: 2014, Director: Ernest Fontich i Xavier Jarque

Subject

Equacions diferencials ordinàries, Varietats (Matemàtica), Treballs de fi de màster

Subject (English)

Ordinary differential equations, Manifolds (Mathematics), Master's theses

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Màster Oficial - Matemàtica Avançada

Citation

SONG, Jieyao. On the local and global phase portrait of the 1-dimensional complex equation $z{\dot}= f (z)$. [consulted: 15 of August of 2026]. Available at: https://hdl.handle.net/2445/63023

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