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Title:Verižni ulomki in Gaussova preslikava
Authors:ID Vučko Jambrović, Janja (Author)
ID Eremita, Daniel (Mentor) More about this mentor... New window
Files:.pdf UN_Vucko_Jambrovic_Janja_2016.pdf (626,80 KB)
MD5: ABF27815DC55F0AE3341871695CC6D42
 
Language:Slovenian
Work type:Undergraduate thesis
Typology:2.11 - Undergraduate Thesis
Organization:FNM - Faculty of Natural Sciences and Mathematics
Abstract:Diplomsko delo je sestavljeno iz dveh delov. V prvem delu so predstavljene osnovne lastnosti verižnih ulomkov in Gaussove preslikave. Drugi del je namenjen študiju Gaussove preslikave in njenih potenc z uporabo navadnih verižnih ulomkov. Med drugim poiščemo vse fiksne točke vseh potenc Gaussove preslikave G in pokažemo, da je graf funkcije G^n z definicijskim območjem [0, 1/2] simetričen grafu funkcije G^n+1 z definicijskim območjem [1/2, 1].
Keywords:verižni ulomek, Gaussova preslikava, končni verižni ulomek, neskončni verižni ulomek, periodični verižni ulomek
Place of publishing:Maribor
Publisher:[J. Vučko Jambrović]
Year of publishing:2016
PID:20.500.12556/DKUM-57311 New window
UDC:517.524(043.2)
COBISS.SI-ID:22596616 New window
NUK URN:URN:SI:UM:DK:UJJPMUWD
Publication date in DKUM:29.09.2016
Views:2092
Downloads:111
Metadata:XML DC-XML DC-RDF
Categories:FF
FNM
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Secondary language

Language:English
Title:Continued fractions and the Gauss map
Abstract:The graduation thesis consists of two parts. In the first part basic properties of continued fractions and the Gauss Map are presented. The second part is devoted to the study of the Gauss Map and its iterates using continued fractions. In particular, we determine all fixed points of all iterates of the Gauss Map G and we show that the graph of G^n over [0, 1/2] is symetric to the graph of G^n+1 over [1/2 , 1].
Keywords:continued fraction, Gauss Map, finite continued fraction, infinite continued fraction, periodic continued fraction


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