Posplošitve markovskih funkcij in njihove inverzne limite

Lunder, Tjaša

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Title:	Posplošitve markovskih funkcij in njihove inverzne limite
Authors:	ID Lunder, Tjaša (Author) ID Banič, Iztok (Mentor) More about this mentor... ID Milutinović, Uroš (Comentor)
Files:	DOK_Lunder_Tjasa_2019.pdf (1,65 MB) MD5: 6F6E8228EE69772D94A20965E352D09C PID: 20.500.12556/dkum/e33600c6-9712-4225-865e-3dc3bf452978
Language:	Slovenian
Work type:	Doctoral dissertation
Typology:	2.08 - Doctoral Dissertation
Organization:	FNM - Faculty of Natural Sciences and Mathematics
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 večličnih preslikav dokaže izrek analogen izreku Holtove v [11]. Izrek Holtove velja samo za surjektivne enolične markovske preslikave. Naš izrek pa velja tudi za večlične 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 večličnih funkcij). V zadnjem poglavju smo predstavili nekaj odprtih problemov.
Keywords:	markovska preslikava, ve£li£na funkcija, navzgor polzvezna funkcija, posplo²ena markovska funkcija, ²tevno markovska funkcija, inverzno zaporedje, inverzna limita, ²otorska funkcija, funkcija oblike N.
Place of publishing:	[Maribor
Publisher:	T. Lunder]
Year of publishing:	2019
PID:	20.500.12556/DKUM-71470
UDC:	515.126(043.3)
COBISS.SI-ID:	24392968
NUK URN:	URN:SI:UM:DK:IRMPFKQE
Publication date in DKUM:	19.02.2019
Views:	1511
Downloads:	171
Metadata:
Categories:	FNM
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Licences

License:	CC BY-NC-ND 4.0, Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International

Link:	http://creativecommons.org/licenses/by-nc-nd/4.0/
Description:	The most restrictive Creative Commons license. This only allows people to download and share the work for no commercial gain and for no other purposes.
Licensing start date:	16.08.2018

Secondary language

Language:	English
Title:	Generalizations of markov maps and their inverse limits
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.
Keywords:	Markov interval map, set-valued function, upper semi-continuous function, generalized Markov function, countably Markov function, inverse sequence, inverse limit, tent function, function of the shape N.

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