Fuchsove grupe
diplomsko delo
Abstract
V diplomskem delu obravnavamo grupo Möbiusovih transformacij kompleksne zgornje polravnine. Njene diskretne podgrupe imenujemo Fuchsove grupe. Definirali bomo pojem osnovnega območja za dano Fuchsovo grupo in videli, da slike osnovnega območja pri delovanju Fuchsove grupe tlakujejo kompleksno zgornjo polravnino. V nadaljevanju bomo konstruirali osnovna območja za dane Fuchsove grupe, imenovana Dirichletovi večkotniki. Sledijo primeri transformacij, ki povezujejo stranice Dirichletovih večkotnikov v pare.
Keywords
matematika;hiperbolična ravnina;transformacije;Fuchsove grupe;osnovno območje;večkotniki;diplomska dela;
Data
| Language: | Slovenian |
|---|---|
| Year of publishing: | 2011 |
| Source: | Maribor |
| Typology: | 2.11 - Undergraduate Thesis |
| Organization: | UM FNM - Faculty of Natural Sciences and Mathematics |
| Publisher: | [M. Žnidarič] |
| UDC: | 51(043.2) |
| COBISS: |
18790408
|
| Views: | 1656 |
| Downloads: | 109 |
| Average score: | 0 (0 votes) |
| Metadata: |
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Other data
| Secondary language: | English |
|---|---|
| Secondary title: | FUCHSIAN GROUPS |
| Secondary abstract: | In the following graduation thesis the group of Möbius transformations of complex upper half-plane are discussed. Its discrete subgroups are called Fuchsian groups. We will define the concept of fundamental domains for a given Fuchsian group and see that the images of the fundamental domain under the Fuchsian group tessellete the complex upper half-plane. Then fundamental domains for given Fuchsian groups will be constructed; those are called Dirichlet polygons. This is followed by examples of Side-pairing transformations for Dirichlet polygon. |
| Secondary keywords: | Hyperbolic plane;Möbius transformations;Fuchsian group;fundamental domain;Dirichlet polygon.; |
| URN: | URN:SI:UM: |
| Type (COBISS): | Undergraduate thesis |
| Thesis comment: | Univ. v Mariboru, Fak. za naravoslovje in matematiko, Oddelek za matematiko in računalništvo |
| Pages: | IX, 38 f. |
| Keywords (UDC): | mathematics;natural sciences;naravoslovne vede;matematika;mathematics;matematika; |
| ID: | 19662 |
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