Topološki Markovljevi lanci

master's thesis

• Author: Grgo Slavica
• Mentor: Pavle Goldstein (mentor)
• Committee member: Pavle Goldstein (predsjednik povjerenstva)
• Committee member: Miljenko Huzak (član povjerenstva)
• Committee member: Nela Bosner (član povjerenstva)
• Committee member: Vedran Krčadinac (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Mathematics); Zagreb
• Defense date and country: 2015-09-23, Croatia
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Mathematics

Abstract

U ovom diplomskom radu se upoznajemo sa pojmom topoloških Markovljevih lanaca i prostorom na kojem su oni definirani. Diplomski rad je podijeljen u dva glavna poglavlja. U prvom poglavlju definiramo pojmove potrebne za definiciju topološkog Markovljevog lanca i navodimo metriku koja će inducirati topologiju na topološkim Markovljevim lancima. Također, upoznali smo se i sa pojmom Markovljeve particije. U drugom poglavlju bavimo se ekvivalencijom toka (eng. flow equivalence) i iznosimo važne teoreme i propozicije vezane za tu temu. Na kraju iznosimo postupak provjere da su dva topološka Markovljeva lanca tok ekvivalentna (Franksov rezultat).

Abstract (english)

In this thesis, we are concerned with topological Markov chains and various equivalence relations defined on them. In the first part, we give the background on metric and topological spaces, introduce topological Markov chains and Markov partitions. In the second part, we define flow equivalence and state several important results regarding flow equivalence characterization. Finally, we state and explain Franks result regarding algebraic invariants of flow equivalence.

• Keywords: topološki Markovljevi lanci; Markovljeva particija; ekvivalencija toka; Markovljev lanac
• Keywords (english): topological Markov chains; Markov partitions; flow equivalence
• Language: croatian
• URN:NBN: urn:nbn:hr:217:272007
• Study programme: Title: Mathematical Statistics; 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: 2019-02-06 15:31:07