prikaz prve stranice dokumenta Topological Surgery and Almost 1-1 Extensions of Dynamical Systems
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master's thesis
Topological Surgery and Almost 1-1 Extensions of Dynamical Systems
2020. urn:nbn:hr:166:925598
Jelić, Domagoj
University of Split
Faculty of Science
Department of Mathematics

Cite this document

Jelić, D. (2020). Topological Surgery and Almost 1-1 Extensions of Dynamical Systems (Master's thesis). Split: University of Split, Faculty of Science. Retrieved from https://urn.nsk.hr/urn:nbn:hr:166:925598

Jelić, Domagoj. "Topological Surgery and Almost 1-1 Extensions of Dynamical Systems." Master's thesis, University of Split, Faculty of Science, 2020. https://urn.nsk.hr/urn:nbn:hr:166:925598

Jelić, Domagoj. "Topological Surgery and Almost 1-1 Extensions of Dynamical Systems." Master's thesis, University of Split, Faculty of Science, 2020. https://urn.nsk.hr/urn:nbn:hr:166:925598

Jelić, D. (2020). 'Topological Surgery and Almost 1-1 Extensions of Dynamical Systems', Master's thesis, University of Split, Faculty of Science, accessed 29 December 2024, https://urn.nsk.hr/urn:nbn:hr:166:925598

Jelić D. Topological Surgery and Almost 1-1 Extensions of Dynamical Systems [Master's thesis]. Split: University of Split, Faculty of Science; 2020 [cited 2024 December 29] Available at: https://urn.nsk.hr/urn:nbn:hr:166:925598

D. Jelić, "Topological Surgery and Almost 1-1 Extensions of Dynamical Systems", Master's thesis, University of Split, Faculty of Science, Split, 2020. Available at: https://urn.nsk.hr/urn:nbn:hr:166:925598

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Metadata
TitleTopological Surgery and Almost 1-1 Extensions of Dynamical Systems
Title (croatian)Topološka kirurgija i skoro 1-1 proširenja dinamičkih sustava
AuthorDomagoj Jelić
MentorPiotr Oprocha (mentor)
Committee memberPiotr Oprocha (predsjednik povjerenstva)
Committee memberGoran Erceg (član povjerenstva)
Committee memberVlasta Matijević (član povjerenstva)
GranterUniversity of Split
Faculty of Science
(Department of Mathematics)
Split
Defense date and country2020-07-28, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Abstract
The main objective of this master’s thesis is to present various applications of topological surgery on dynamical systems. We show examples in which from well-known dynamical systems, using only topological manipulations, we obtain new dynamical systems with desired properties as almost 1-1 extensions of the original systems. Namely, by inverse limit technique we present how to prove the existence of points not belonging to stable continua. Furthermore, by similar techniques we construct spaces of different types considering the admittance of a minimal homeomorphism and a minimal noninvertible map. We also construct spaces admitting minimal homeomorphisms whose Cartesian powers do not admit minimal homeomorphisms. For the end, by similar techniques, we show the existence of spaces with cyclic homeomorphism groups generated by minimal homeomorphisms, as well as existence of minimal spaces with degenerate homeomorphism groups.
Abstract (croatian)
Glavni cilj ovog rada je predstaviti različite primjene topološke kirurgije u dinamičkim sustavima. Dajemo primjere u kojima iz poznatih dinamičkih sustava, korištenjem isključivo topoloških manipulacija, dobivamo nove dinamičke sustave sa željenim svojstvima kao skoro 1-1 proširenja početnih. Preciznije, tehnikom inverznog limesa pokazujemo kako dokazati postojanje točaka koje ne pripadaju stabilnim kontinuumima. Nadalje, sličnim tehnikama konstruiramo prostore različitih tipova s obzirom na dopuštanje minimalnih homeomorfizama, odnosno minimalnih neinvertibilnih neprekidnih preslikavanja. Također, konstruiramo i prostore koji dopuštaju minimalne homeomorfizme, za razliku od njihovih Kartezijevih potencija. Za kraj, sličnim tehnikama pokazujemo postojanje prostora s cikličkom grupom homeomorfizama generiranom minimalnim homeomorfizmom, kao i postojanje minimalnih prostora s trivijalnom grupom homeomorfizama.
Keywords
Keywords (croatian)
Languageenglish
URN:NBNurn:nbn:hr:166:925598
Study programmeTitle: Mathematics; specializations in: major in pure mathematics, major in computing, major in teaching, major in statistics and computing
Course: major in pure mathematics
Study programme type: university
Study level: graduate
Academic / professional title: magistar/magistra matematike (magistar/magistra matematike)
Type of resourceText
File originBorn digital
Access conditionsAccess restricted to students and staff of home institution
Terms of useLicence In copyright icon
Created on2021-02-02 15:48:10