doktorska disertacija
Tjaša Lunder (Author), Iztok Banič (Mentor), Matevž Črepnjak (Thesis defence commission member), Uroš Milutinović (Co-mentor)

Abstract

Disertacija se ukvarja s študijem posebnih tipov posplošenih inverznih limit. V disertaciji smo uspešno rešili problem izbire definicije posplošenih markovskih funkcij in definicije enakosti vzorcev dveh takšnih funkcij, ki nam omogoča, da se tudi za razred več ličnih preslikav dokaže izrek analogen izreku Holtove v [11]. Izrek Holtove velja samo za surjektivne enolične markovske preslikave. Naš izrek pa velja tudi za več lične funkcije, velja celo brez predpostavke o surjektivnosti. Tako pri markovskih preslikavah kot pri naših, posplošenih markovskih preslikavah, so particije končne množice. V nadaljevanju disertacije smo pokazali, da je možna tudi nadaljnja posplošitev, pri kateri so particije števno neskončne. Na ta način smo vpeljali števno markovske funkcije ter enakost vzorcev števno markovskih preslikav. Tudi ti dve definiciji sta bili ustvarjeni tako, da sta omogočili dokaz izreka o homeomorfnosti posplošenih inverznih limit v primeru, kadar so vezne preslikave števno markovske funkcije z enakimi vzorci. Tudi ta izrek smo dokazali brez predpostavke o surjektivnosti. To teorijo smo v nadaljevanju aplicirali na šotorske funkcije in funkcije oblike N (dva posebna razreda enoličnih in več ličnih funkcij). V zadnjem poglavju smo predstavili nekaj odprtih problemov.

Keywords

disertacije;markovska preslikava;večlična funkcija;navzgor polzvezna funkcija;posplošena markovska funkcija;števno markovska funkcija;inverzno zaporedje;inverzna limita;šotorska funkcija;funkcija oblike N;

Data

Language: Slovenian
Year of publishing:
Typology: 2.08 - Doctoral Dissertation
Organization: UM FNM - Faculty of Natural Sciences and Mathematics
Publisher: T. Lunder]
UDC: 515.126(043.3)
COBISS: 24392968 Link will open in a new window
Views: 889
Downloads: 93
Average score: 0 (0 votes)
Metadata: JSON JSON-RDF JSON-LD TURTLE N-TRIPLES XML RDFA MICRODATA DC-XML DC-RDF RDF

Other data

Secondary language: English
Secondary title: Generalizations of markov maps and their inverse limits
Secondary abstract: The doctoral dissertation studies special types of generalized inverse limits. In the dissertation we successfully solved the problem of a good choise for the definition of generalized Markov functions and the definition of the same pattern of two such functions, which enables us to prove an analogue Theorem as in [11] for set-valued functions. Holte's Theorem refers only to surjective single-valued Markov functions. Our Theorem refers to set-valued functions, even without the assumption of surjectivity. Markov functions as well as ours, generalized Markov functions, have finite partitions. In the next part of the doctoral dissertation we have proven, that a further generalization is possible, where the partitions are countable infinite. With this we introduced countably Markov functions and the same pattern of two such functions. These two definitions have been created to enable us to prove the Theorem of homeomorficness of generalized inverse limits when the bonding functions are countably Markov functions with the same pattern. This theorem has also been proven without the assumption of surjectivity. We have applied this Theory to tent functions and functions of the shape N (two special types of single-valued and set-valued functions). In the last chapter we introduced some open problems.
Secondary keywords: Markov interval map;set-valued function;upper semi-continuous function;generalized Markov function;countably Markov function;inverse limit;tent function;function of the shape N;dissertations;
URN: URN:SI:UM:
Type (COBISS): Doctoral dissertation
Thesis comment: Univ. v Mariboru, Fak. za naravoslovje in matematiko, Oddelek za matematiko in računalništvo
Pages: II, 81 f.
ID: 10950960