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master's thesis
Martellijev kaos u dinamičkim sustavima na inverznim limesima i hiperprostorima
Zagreb: University of Zagreb, Faculty of Science, 2014. urn:nbn:hr:217:965740
Trpčić, Maja
University of Zagreb
Faculty of Science
Department of Mathematics

Institutional repository: Repository of the Faculty of Science

Cite this document

Trpčić, M. (2014). Martellijev kaos u dinamičkim sustavima na inverznim limesima i hiperprostorima (Master's thesis). Zagreb: University of Zagreb, Faculty of Science. Retrieved from https://urn.nsk.hr/urn:nbn:hr:217:965740

Trpčić, Maja. "Martellijev kaos u dinamičkim sustavima na inverznim limesima i hiperprostorima." Master's thesis, University of Zagreb, Faculty of Science, 2014. https://urn.nsk.hr/urn:nbn:hr:217:965740

Trpčić, Maja. "Martellijev kaos u dinamičkim sustavima na inverznim limesima i hiperprostorima." Master's thesis, University of Zagreb, Faculty of Science, 2014. https://urn.nsk.hr/urn:nbn:hr:217:965740

Trpčić, M. (2014). 'Martellijev kaos u dinamičkim sustavima na inverznim limesima i hiperprostorima', Master's thesis, University of Zagreb, Faculty of Science, accessed 03 November 2024, https://urn.nsk.hr/urn:nbn:hr:217:965740

Trpčić M. Martellijev kaos u dinamičkim sustavima na inverznim limesima i hiperprostorima [Master's thesis]. Zagreb: University of Zagreb, Faculty of Science; 2014 [cited 2024 November 03] Available at: https://urn.nsk.hr/urn:nbn:hr:217:965740

M. Trpčić, "Martellijev kaos u dinamičkim sustavima na inverznim limesima i hiperprostorima", Master's thesis, University of Zagreb, Faculty of Science, Zagreb, 2014. Available at: https://urn.nsk.hr/urn:nbn:hr:217:965740

Metadata
TitleMartellijev kaos u dinamičkim sustavima na inverznim limesima i hiperprostorima
AuthorMaja Trpčić
MentorSonja Štimac (mentor)
Committee memberSonja Štimac (predsjednik povjerenstva)
Committee memberSiniša Slijepčević (član povjerenstva)
Committee memberMladen Jurak (član povjerenstva)
Committee memberVjeran Hari (član povjerenstva)
GranterUniversity of Zagreb
Faculty of Science
(Department of Mathematics)
Zagreb
Defense date and country2014-07-14, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Abstract
Na početku rada navodimo neke osnovne definicije i pojmove, koji će nam biti potrebni u nastavku rada. Upoznajemo se s različitim definicijama kaosa, te promatramo odnos između njih. Definiramo neka poznata preslikavanja te pokazujemo da su kaotična. U drugom poglavlju promatramo Martellijev kaos na inverznim limesima. Navodimo definicije, te kroz nekoliko teorema dokazujemo da je inverzni limes s preslikavanjem pomaka Martellijev kaos ako i samo ako je originalni sustav s veznim preslikavanjem Martelijev kaos. Navodimo i dva primjera kroz koja prikazujemo navedene tvrdnje. Na kraju promatramo Martellijev kaos na hiperprostorima. Kao i u prethodnom poglavlju navodimo definiciju, te nakon toga kroz nekoliko teorema dokazujemo da ako je hiperprostor Martellijev kaos i ako je svaka točka originalnog sustava nestabilna u hiperprostoru, tada je i originalni sustav Martellijev kaos.
Abstract (english)
At the very beginning of this paper we introduce some basic definitions and concepts, which we will need in sequel. We define different definitions of chaos, and observe the relationship between them. We define some familiar mappings and show that they are chaotic. In the second chapter we investigate Martelli’s chaos of inverse limit dynamical systems. We give definitions, and through a few theorems we prove that inverse limit dynamical system is Martelli’s chaos if and only if so is original system. Here are two examples that illustrate listed properties. Finally, we investigate Martelli’s chaos of hyperspace dynamical systems. As in the previous chapter we give some definitions, and through a few theorems we prove that hyperspace dynamical system is Martelli’s chaos implies original system is Martelli’s chaos if the orbit of every single point set of original system is unstable in hyperspace.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:217:965740
Study programmeTitle: Mathematical Statistics
Study programme type: university
Study level: graduate
Academic / professional title: magistar/magistra matematike (magistar/magistra matematike)
Type of resourceText
File originBorn digital
Access conditionsOpen access
Terms of useLicence In copyright icon
Created on2019-02-18 11:23:54