diplomsko delo
Janja Vučko Jambrović (Author), Daniel Eremita (Mentor)

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 $[0, frac{1}{2}]$ simetričen grafu funkcije $G^{n+1}$ z definicijskim območjem $[frac{1}{2}, 1]$.

Keywords

verižni ulomek;Gaussova preslikava;končni verižni ulomek;neskončni verižni ulomek;periodični verižni ulomek;diplomska dela;

Data

Language: Slovenian
Year of publishing:
Typology: 2.11 - Undergraduate Thesis
Organization: UM FNM - Faculty of Natural Sciences and Mathematics
Publisher: [J. Vučko Jambrović]
UDC: 517.524(043.2)
COBISS: 22596616 Link will open in a new window
Views: 1115
Downloads: 62
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Other data

Secondary language: English
Secondary title: Continued fractions and the Gauss map
Secondary 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, frac{1}/{2}] is symetric to the graph of $G^{n+1}$ over $[frac{1}{2}, 1]$.
Secondary keywords: continued fraction;Gauss Map;finite continued fraction;infinite continued fraction;periodic continued fraction;theses;
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, 37 f.
ID: 9123670