Izrek o izravnavi : delo diplomskega seminarja

Sfiligoj, Anže (author), Kuzman, Uroš (mentor)

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.

• Language: Slovenian
• Keywords: negibna točka, Juliajeva množica, Fatoujeva množica, kvazikonformna preslikava, dilatacija, Beltramijeva enačba, izrek o izravnavi, polinomu podobna preslikava
• Work type: Final seminar paper
• Organization: FMF - Faculty of Mathematics and Physics
• Year: 2019
• PID: 20.500.12556/RUL-110802
• UDC: 517.5
• COBISS.SI-ID: 18816601
• Publication date in RUL: 20.09.2019

Secondary language

• Language: English
• Title: Straightening theorem

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.

• Keywords: fixed point, Julia set, Fatou set, quasiconformal mapping, dilatation, Beltrami equation, straightening theorem, polynomial-like mapping