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Constructing Multidimensional Dynamical Systems with Positive Lyapunov Exponents
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
2018 (English)Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesisAlternative title
Konstruktion av Flerdimensionella Dynamiska System med Positiva Lyapunovexponenter (Swedish)
Abstract [en]

In this thesis we adapt Marcelo Viana's general construction of smooth transformations exhibiting non-uniform expansion in several dimensions. In our construction we, instead of coupling with a quadratic map, as Viana did, derive the expansion from a mapping with a cubic critical point. Further, we discuss how the argument can be extended and expansion derived from certain mappings with a critical point of arbitrarily high (odd) degree. We also discuss the issues in trying to use Viana's method with the double standard map as our source of non-uniform expansion.

Abstract [sv]

I denna uppsats anpassar vi Marcelo Vianas generella konstruktion av  glatta transformationer som uppvisar icke-likformig expansion i flera  dimensioner. I vår konstruktion, istället för att koppla ihop vårt system med en kvadratisk avbildning, får vi expansionen från en avbildning med en  kubisk kritisk punkt. Dessutom så diskuterar vi hur argumentationen kan  utvidgas och expansionen fås av vissa typer av avbildningar med en kritisk punkt av godtyckligt hög (udda) grad. Vi diskuterar också problemen i att försöka använda Vianas metod med den så kallade "double standard"-avbildningen som källan till den icke-likformiga expansionen.

Place, publisher, year, edition, pages
2018.
Series
TRITA-SCI-GRU ; 2018:255
National Category
Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-229973OAI: oai:DiVA.org:kth-229973DiVA, id: diva2:1219255
Subject / course
Mathematics
Educational program
Master of Science - Mathematics
Supervisors
Examiners
Available from: 2018-06-15 Created: 2018-06-15 Last updated: 2018-06-15Bibliographically approved

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