Topološki stupanj

master's thesis

• Author: Lucija Štefanić
• Mentor: Eduard Marušić-Paloka (mentor)
• Committee member: Eduard Marušić-Paloka (predsjednik povjerenstva)
• Committee member: Boris Širola (član povjerenstva)
• Committee member: Juraj Šiftar (član povjerenstva)
• Committee member: Mirko Primc (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Mathematics); Zagreb
• Defense date and country: 2015-02-27, Croatia
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Mathematics

Abstract

U ovom radu uveden je pojam topološkog stupnja. Navedena su njegova osnovna svojstva te je opisana njegova konstrukcija. Konstrukcija se razlikuje ovisno o konačnosti dimenzije prostora na kojem je stupanj definiran. U slučaju konačne dimenzije topološki stupanj nazivamo Brouwerovim stupnjem, a u beskonačnodimenzionalnom slučaju Leray-Schauderov stupanj. Izneseni su neki važni teoremi koji podupiru teoriju stupnja kao što su Brouwerov teorem o fiksnoj točki te Schauderov teorem o fiksnoj točki. Kao primjer primjene stupnja naveden je topološki problem bifurkacije.

Abstract (english)

The objective of the present thesis is to define topological degree and it’s construction. Depending on the dimension of the space there are different constructions. In finitedimensional space we are talking about Brouwer’s degree, while in infinite-dimensional space it is Leray-Schauder’s degree. Important theorems for this theory are given. As an example for application of topological degree it is mentioned and explained topological problem of bifurcation.

• Keywords: topološki stupanj; Brouwerov stupanj; Leray-Schauderov stupanj; Brouwerov teorem o fiksnoj točki; Schauderov teorem o fiksnoj točki; topološki problem bifurkacije
• Keywords (english): topological degree; Brouwer’s degree; Leray-Schauder’s degree; Brouwer fixt poin theorem; Schauder fixt poin theorem; topological problem of bifurcation
• Language: croatian
• URN:NBN: urn:nbn:hr:217:480179
• Study programme: Title: Finance and Business Mathematics; Study programme type: university; Study level: graduate; Academic / professional title: magistar/magistra matematike (magistar/magistra matematike)
• Type of resource: Text
• File origin: Born digital
• Access conditions: Open access
• Created on: 2019-02-14 09:28:04