Original title: Chaos a intervalová dynamika
Translated title: Chaos and interval dynamics
Authors: Smerčiak, Samuel ; Vejnar, Benjamin (advisor) ; Bobok, Jozef (referee)
Document type: Bachelor's theses
Year: 2024
Language: slo
Abstract: [eng] [cze]
This bachelor thesis is mainly concerned with the Sharkovsky theorem. Initially, we define basic concepts from the theory of discrete dynamical systems, followed by a proof of the Sharkovsky theorem based on the examination of the covering relation between the elements of the partition of the interval corresponding to a periodic orbit. Next we concentrate on the stability of the Sharkovsky theorem with respect to the topology of uniform convergence on the space of continuous functions. Lastly, we indicate possible extensions of the Sharkovsky theorem, emphasizing the case of triangular maps. V tejto práci sa zaoberáme predovšetkým Šarkovského vetou. Na úvod definujeme základné pojmy z teórie diskrétnych dynamických systémov a následne podáme dôkaz Šarkovského vety založený na skúmaní relácie pokrývania medzi prvkami delenia inter- valu príslušného periodickej orbite. Ďalej sa zameriame na stabilitu Šarkovského vety vzhľadom k topológii rovnomernej konvergencie na priestore spojitých funkcií. Nakoniec poukážeme na možné rozšírenia Šarkovského vety s dôrazom na prípad trojuholníkových zobrazení.
Keywords: dynamical system|continuous mapping|ordering; dynamický systém|spojitá funkce|uspořádání

Institution: Charles University Faculties (theses) (web)
Document availability information: Available in the Charles University Digital Repository.
Original record: http://hdl.handle.net/20.500.11956/191195

Permalink: http://www.nusl.cz/ntk/nusl-621327


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Universities and colleges > Public universities > Charles University > Charles University Faculties (theses)
Academic theses (ETDs) > Bachelor's theses