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Title:FUCHSOVE GRUPE
Authors:ID Žnidarič, Maja (Author)
ID Pagon, Dušan (Mentor) More about this mentor... New window
Files:.pdf UNI_Znidaric_Maja_2011.pdf (599,33 KB)
MD5: 7094032F9687F8E826C2F3FA893B17A1
PID: 20.500.12556/dkum/15d58042-6251-4323-b6dd-538da663c19f
 
Language:Slovenian
Work type:Undergraduate thesis
Organization:FNM - Faculty of Natural Sciences and Mathematics
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:Hiperbolična ravnina, Möbiusova transformacija, Fuchsova grupa, osnovno območje, Dirichletov večkotnik.
Place of publishing:Maribor
Publisher:[M. Žnidarič]
Year of publishing:2011
PID:20.500.12556/DKUM-21219 New window
UDC:51(043.2)
COBISS.SI-ID:18790408 New window
NUK URN:URN:SI:UM:DK:IGR0HNNU
Publication date in DKUM:30.11.2011
Views:2323
Downloads:149
Metadata:XML DC-XML DC-RDF
Categories:FNM
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Secondary language

Language:English
Title:FUCHSIAN GROUPS
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.
Keywords:Hyperbolic plane, Möbius transformations, Fuchsian group, fundamental domain, Dirichlet polygon.


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