Izrek o izravnavi
delo diplomskega seminarja
Abstract
Kompleksna dinamika je področje matematike, ki se ukvarja z dinamičnimi sistemi definiranimi z iteracijami kompleksnih preslikav. V tem diplomskem delu se osredotočimo na kompleksne preslikave s polinomsko dinamiko in izrek o izravnavi. Definirali bomo razred preslikav, ki se na neki podmnožici svoje domene obnašajo kot polinomska preslikava. Z uporabo kvazikonformnih preslikav bomo dokazali izrek o izravnavi, ki pove, da imajo take preslikave enake dinamične lastnosti kot polinomi.
Keywords
matematika;negibne točke;Juliajeva množica;Fatoujeva množica;kvazikonformne preslikave;dilatacije;Beltramijeva enačba;izrek o izravnavi;polinomu podobna preslikava;
Data
| Language: | Slovenian |
|---|---|
| Year of publishing: | 2019 |
| Typology: | 2.11 - Undergraduate Thesis |
| Organization: | UL FMF - Faculty of Mathematics and Physics |
| Publisher: | [A. Sfiligoj] |
| UDC: | 517.5 |
| COBISS: |
18816601
|
| Views: | 1137 |
| Downloads: | 236 |
| Average score: | 0 (0 votes) |
| Metadata: |
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Other data
| Secondary language: | English |
|---|---|
| Secondary title: | Straightening theorem |
| Secondary abstract: | Complex dynamics is the study of dynamical systems defined by iterations of complex mappings. We focus on complex mappings with polynomial dynamics in this diploma. We will define a class of mappings, which behave like a polynomial mapping on some subset of their domain. Using quasiconformal mappings we will prove the straightening theorem, which states that these mappings have the same dynamical properties as polynomials. |
| Secondary keywords: | mathematics;fixed points;Julia set;Fatou set;quasiconformal mappings;dilatation;Beltrami equation;straightening theorem;polynomial-like mappings; |
| 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: | 26 str. |
| ID: | 11229071 |
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