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An analysis of a shared mating in V2.
Umeå University, Faculty of Science and Technology, Department of Physics.
2014 (English)Independent thesis Advanced level (degree of Master (One Year)), 20 credits / 30 HE creditsStudent thesis
Abstract [en]

In this master thesis we investigate, from a topological point of view and without applying Thurston´s Theorem, why the mating of the so called basilica polynomial  and the dendrite  is shared with the mating of  and the dendrite . Both these matings equal the rational map .

Defined in the thesis are for both matings homeomorphic changes of coordinates from the set  to the Fatou and Julia set of . Here  is the filled Julia set of  and is the -fixed point of .

Abstract [sv]

I detta examensarbete undersöker vi, från en topologisk synvinkel och utan applicering av Thurstons teorem, varför matchningen av det så kallade basilikapolynomet

 och dendriten  är delad med matchningen av  och dendriten .

Båda dessa matchningar är lika med den rationella avbildningen


Definierat i examensarbetet är för båda matchningarna homoemorfa koordinatbyten från mängden till Fatou- och Juliamängden av . Här är  den ifyllda Juliamängden av avbildningen  och  är den -fixerade punkten i .

Place, publisher, year, edition, pages
2014. , 57 p.
Keyword [en]
Complex dynamics mating matings basilica dendrite Julia Fatou
Keyword [sv]
komplex dynamik matchning matchningar basilika dendrit Juliamängd Fatoumängd
National Category
Mathematical Analysis
URN: urn:nbn:se:umu:diva-96855OAI: diva2:768806
External cooperation
Matematikcentrum, Lunds Universitet.
Subject / course
Examensarbete i teknisk fysik
Educational program
Master of Science Programme in Engineering Physics
2014-11-14, Universitetsklubben, Universum , 907 19, Umeå, 13:00 (English)
Available from: 2014-12-05 Created: 2014-12-04 Last updated: 2014-12-05Bibliographically approved

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