Kvazikonformna kirurgija in Hermanovi kolobarji

delo diplomskega seminarja

Beno Učakar (Author), Uroš Kuzman (Mentor)

Abstract

Kompleksna dinamika je področje matematike, ki se ukvarja z dinamičnimi sistemi določenimi z iteracijo kompleksnih preslikav. Cilj diplomske naloge je konstruirati racionalno preslikavo, katere dinamika je na 2-povezanem območju biholomorfno ekvivalentna iracionalni rotaciji. Tak fenomen imenujemo Hermanov kolobar. Najprej se seznanimo z osnovami kompleksne dinamike in opredelimo pojem Hermanovega kolobarja. Nato razvijemo teorijo kvazikonformnih preslikav in s pomočjo kvazikonformne kirurgije kostruiramo racionalno preslikavo, ki premore Hermanov kolobar.

Keywords

matematika;kompleksna dinamika;negibne točke;Juliajeve množice;Fatoujeve množice;Siegelov disk;Hermanov kolobar;kvazikonformne preslikave;Beltramijeva enačba;eliptična polja;kvazikonformna kirurgija;

Data

Language:	Slovenian
Year of publishing:	2022
Typology:	2.11 - Undergraduate Thesis
Organization:	UL FMF - Faculty of Mathematics and Physics
Publisher:	[B. Učakar]
UDC:	517
COBISS:	118585859
Views:	1626
Downloads:	193
Average score:	0 (0 votes)
Metadata:

Other data

Secondary language:	English
Secondary title:	Quasiconformal surgery and Herman rings
Secondary abstract:	Complex dynamics is the study of dynamical systems defined by the iteration of complex valued functions. The goal of this thesis is to construct a rational function with dynamics on a 2-connected region biholomorphically equivalent to an irrational rotation. This phenomenon is called a Herman ring. First we familiarize ourselves with the basics of complex dynamics and define the term Herman ring. Then we develop the theory of quasiconformal maps and with the help of quasiconformal surgery construct a rational function with a Herman ring.
Secondary keywords:	mathematics;complex dynamics;fixed points;Julia sets;Fatou sets;Siegel disk;Herman ring;quasiconformal mappings;Beltrami equation;elliptic fields;quasiconformal surgery;
Type (COBISS):	Final seminar paper
Study programme:	0
Embargo end date (OpenAIRE):	1970-01-01
Thesis comment:	Univ. v Ljubljani, Fak. za matematiko in fiziko, Oddelek za matematiko, Matematika - 1. stopnja
Pages:	32 str.
ID:	16154913